A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538–1541 (1997).

[CrossRef]

M. Shih, M. Segev, and G. Salamo, “Three-dimensional spiralling of interacting spatial solitons,” Phys. Rev. Lett. 78, 2551–2554 (1997).

[CrossRef]

A. W. Snyder and D. J. Mitchell, “Mighty morphing spatial solitons and bullets,” Opt. Lett. 22, 16–18 (1997).

[CrossRef]
[PubMed]

W. Krolikowski and S. A. Holmstrom, “Fusion and birth of spatial solitons upon collision,” Opt. Lett. 22, 369–371 (1997).

[CrossRef]
[PubMed]

M. Shih, M. Segev, and G. Salamo, “Circular waveguides induced by two-dimensional bright steady-state photorefractive screening solitons,” Opt. Lett. 21, 931–933 (1996).

[CrossRef]
[PubMed]

M. Shih and M. Segev, “Incoherent collision between two-dimensional bright steady-state photorefractive spatial screening solitons,” Opt. Lett. 21, 1538–1540 (1996).

[CrossRef]
[PubMed]

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three-dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76, 2698–2701 (1996).

[CrossRef]
[PubMed]

D. E. Pelinovsky, Yu. S. Kivshar, and V. V. Afanasjev, “Instability-induced dynamics of dark solitons,” Phys. Rev. E 53, 2015–2032 (1996).

[CrossRef]

D. E. Pelinovsky, V. V. Afanasjev, and Yu. S. Kivshar, “Nonlinear theory of oscillating, decaying, and collapsing solitons in the generalized nonlinear Schrödinger equation,” Phys. Rev. E 52, 1940–1953 (1996).

[CrossRef]

A. V. Buryak, Yu. S. Kivshar, and D. F. Parker, “Coupling between bright and dark solitons,” Phys. Lett. A 215, 57–62 (1996).

[CrossRef]

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, “Stability of three-wave parametric solitons in diffractive quadratic media,” Phys. Rev. Lett. 77, 5210–5213 (1996); A. V. Buryak and Yu. S. Kivshar, “Multistability of three-wave parametric self-trapping,” Phys. Rev. Lett. 78, 3286–3289 (1997); C. Etrich, U. Peschel, F. Lederer, and B. A. Malomed, “Stability of temporal chirped solitary waves in quadratically nonlinear media,” Phys. Rev. E 55, 6155–6161 (1997).

[CrossRef]
[PubMed]

A. W. Snyder, D. J. Mitchell, and A. V. Buryak, “Qualitative theory of bright solitons—the soliton sketch,” J. Opt. Soc. Am. B 13, 1146–1150 (1996).

[CrossRef]

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, “Observation of Manakov spatial solitons in AlGaAs planar waveguides,” Phys. Rev. Lett. 76, 3699–3702 (1996).

[CrossRef]
[PubMed]

Yu. S. Kivshar, V. V. Afanasjev, and A. W. Snyder, “Dark-like bright solitons,” Opt. Commun. 126, 348–356 (1996).

[CrossRef]

A. W. Snyder, “The linear perspective to soliton dynamics,” Opt. Photonics News 7(12), 27–28 (1996).

[CrossRef]

For the most recent overview of the experimental observations of spatial optical solitons, see the paper by G. I. Stegeman, “The growing family of spatial solitons,” Opt. Appl. 26, 240–248 (1996).

D. J. Mitchell, A. W. Snyder, and L. Poladian, “Interacting self-guided beams viewed as particles: Lorentz force derivation,” Phys. Rev. Lett. 77, 271–273 (1996).

[CrossRef]
[PubMed]

A. W. Snyder, D. J. Mitchell, and Yu. S. Kivshar, “Unification of linear and nonlinear guided wave optics,” Mod. Phys. Lett. B 9, 1479–1506 (1995).

[CrossRef]

A. W. Snyder, S. Hewlett, and D. J. Mitchell, “Periodic solitons in optics,” Phys. Rev. E 51, 6297–6300 (1995).

[CrossRef]

A. W. Snyder, D. J. Mitchell, and M. Haelterman, “Parallel spatial solitons,” Opt. Commun. 116, 365–368 (1995).

[CrossRef]

D. E. Pelinovsky, A. V. Buryak, and Yu. S. Kivshar, “Instability of solitons governed by quadratic nonlinearities,” Phys. Rev. Lett. 75, 591–595 (1995).

[CrossRef]
[PubMed]

L. Torner, C. R. Menyuk, W. E. Torruellas, and G. I. Stegeman, “Two-dimensional solitons with second-harmonic nonlinearity,” Opt. Lett. 20, 13–15 (1995); A. V. Buryak, Yu. S. Kivshar, and V. V. Steblina, “Self-trapping of light beams and parametric solitons in diffractive quadratic media,” Phys. Rev. A 52, 1670–1674 (1995).

[CrossRef]
[PubMed]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).

[CrossRef]
[PubMed]

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Spiraling bright spatial solitons formed by the breakup of an optical vortex in a saturable self-focusing medium,” J. Opt. Soc. Am. B 12, 2046–2052 (1995).

[CrossRef]

A. W. Snyder, S. Hewlett, and D. J. Mitchell, “Dynamic spatial solitons,” Phys. Rev. Lett. 72, 1012–1016 (1994).

[CrossRef]
[PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994); M. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salamo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons,” Opt. Lett. 21, 324–326 (1996).

[CrossRef]
[PubMed]

M. D. Iturbe-Castillo, P. A. Marquez Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).

[CrossRef]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping in an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).

[CrossRef]
[PubMed]

A. W. Snyder and A. P. Sheppard, “Collisons, steering and guidance with spatial solitons,” Opt. Lett. 18, 482–484 (1993).

[CrossRef]
[PubMed]

D. J. Mitchell and A. W. Snyder, “Stability of fundamental nonlinear guided waves,” J. Opt. Soc. Am. B 10, 1572–1580 (1993); applicable to all nonlinearities and also in the presence of waveguide structures.

[CrossRef]

D. Hart and E. M. Wright, “Stability of the TE0 guided wave of a nonlinear waveguide with a self-defocusing bounding medium,” Opt. Lett. 17, 121–123 (1992).

[CrossRef]
[PubMed]

In a defocusing Kerr medium, the only known stable soliton is “a black spatial soliton of circular cross section” (sometimes called a vortex soliton; see Ref. 10), first predicted in optics in the paper by A. W. Snyder, L. Poladian, and D. J. Mitchell, “Stable black self-guided beams of circular symmetry in a bulk Kerr medium,” Opt. Lett. 17, 789–791 (1992). This letter is also the first to suggest such solitons as suitable for guiding signals.

[CrossRef]
[PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).

[CrossRef]
[PubMed]

M. Shalaby and A. J. Barthelemy, “Observation of the self-guided propagation of a dark and bright spatial soliton pair in a focusing nonlinear medium,” IEEE J. Quantum Electron. 28, 2736–2741 (1992).

[CrossRef]

A. W. Snyder, D. J. Mitchell, and F. Ladouceur, “Self-induced optical fibers: spatial solitary waves,” Opt. Lett. 10, 21–23 (1991).

[CrossRef]

D. J. Mitchell, A. W. Snyder, and L. Poladian, “Self-guided beam interaction: method of invariants,” Electron. Lett. 27, 848–849 (1991).

[CrossRef]

L. Poladian, A. W. Snyder, and D. J. Mitchell, “Spiralling spatial solitons,” Opt. Commun. 85, 59–62 (1991).

[CrossRef]

J. T. Manassah, “Induced waveguiding effects in a two-dimensional nonlinear medium,” Opt. Lett. 16, 587–589 (1991).

[CrossRef]
[PubMed]

T. Thwaites, “Will optical fibres become obsolete?” New Scientist, January12, 1991, p. 14.

N. N. Akhmediev, V. M. Eleonsky, N. E. Kulagin, and L. P. Shil’nikov, “Steady-state pulses in a birefringent nonlinear optical fibers: soliton multiplication process,” Pis’ma Zh. Tekh. Fiz. 15, 19–23 (1989) [Sov. Tech. Phys. Lett. 15, 587–588 (1989)]; M. Haelterman and A. P. Sheppard, “Bifurcation phenomena and multiple soliton-bound states in isotropic Kerr media,” Phys. Rev. E 49, 3376–3381 (1994).

[CrossRef]

D. N. Christodoulides and R. I. Joseph, “Vector solitons in birefringent nonlinear dispersive media,” Opt. Lett. 13, 53–55 (1988); M. V. Tratnik and J. E. Sipe, “Bound solitary waves in a birefringent optical fiber,” Phys. Rev. A 38, 2011–2017 (1988); S. Trillo, S. Wabnitz, E. M. Wright, and G. Stegeman, “Optical solitary waves induced by cross-phase modulation,” Opt. Lett. 13, 871–873 (1988).

[CrossRef]
[PubMed]

C. K. R. T. Jones and J. Moloney, “Instability of standing waves in nonlinear optical waveguides,” Phys. Lett. A 117, 175–180 (1986).

[CrossRef]

M. I. Weinstein, “Lyapunov stability of ground state of nonlinear evolution equations,” SIAM J. Math. Anal. 16, 472–483 (1985).

[CrossRef]

P. K. Kaw, K. Nishikawa, Y. Yoshida, and A. Hasegawa, “Two-dimensional and three-dimensional envelope solitons,” Phys. Rev. Lett. 35, 88–91 (1975); J. Z. Wilcox and T. J. Wilcox, “Stability of localized plasma model in two and three dimensions,” Phys. Rev. Lett. 34, 1160–1163 (1975).

[CrossRef]

Yu. N. Karamzin and A. P. Sukhorukov, “Mutual focusing of high-power light beams in media with quadratic nonlinearity,” Zh. Eksp. Teor. Fiz. 68, 834–847 (1975) [Sov. Phys. JETP 41, 414–420 (1976)]; A. V. Buryak and Yu. S. Kivshar, “Spatial optical solitons governed by quadratic nonlinearity,” Opt. Lett. 19, 1612–1614 (1994); L. Torner, C. R. Menyuk, and G. I. Stegeman, “Excitation of solitons with cascaded χ(2) nonlinearity,” Opt. Lett. 19, 1615–1617 (1994).

[CrossRef]
[PubMed]

S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Sov. Phys. JETP 38, 248–253 (1974) [Zh. Eksp. Teor. Fiz. 65, 505–516 (1973)].

M. G. Vakhitov and A. A. Kolokolov, “Stationary solutions of the wave equation in a medium with nonlinearity saturation,” Radiophys. Quantum Electron. 16, 783–789 (1973); applies only for a Kerr medium and no waveguide structures.

[CrossRef]

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Zh. Eksp. Teor. Fiz. 61, 118–134 (1971) [Sov. Phys. JETP 34, 62–69 (1972)].

A. L. Berkhoer and V. E. Zakharov, “Self-excitation of waves with different polarizations in nonlinear media,” Sov. Phys. JETP 31, 486–493 (1970) [Zh. Eksp. Teor. Fiz. 58, 903–911 (1970)].

See, e.g., J. H. Marburger and E. L. Dawes, “Dynamic formation of a small-scale filament,” Phys. Rev. Lett. 21, 556–558 (1968); E. L. Dawes and J. H. Marburger, “Computer studies in self-focusing,” Phys. Rev. 179, 862–868 (1969).

[CrossRef]

S. A. Akhmanov, A. P. Sukhorukov, and R. V. Khokhlov, “Self-focusing and self-trapping of intense light beams in a nonlinear medium,” Sov. Phys. JETP 23, 1025–1033 (1966) [Zh. Eksp. Teor. Fiz. 50, 1537–1549 (1966)].

P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15, 1005–1008 (1965).

[CrossRef]

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–480 (1964).

[CrossRef]

The use of the nonlinearity-induced refractive-index change created by an intense beam for guiding particles (electrons and atoms) was suggested even earlier; see G. A. Askar’yan, “Effect of the gradient of a strong electromagnetic beam on electrons and atoms,” Sov. Phys. JETP 15, 1088–1090 (1962) [Zh. Eksp. Teor. Fiz. 42, 1567–1570 (1962)].

J. B. Keller, “The geometrical theory of diffraction,” J. Opt. Soc. Am. 12, 116–130 (1962).

[CrossRef]

As spatially localized solutions of the defocusing cubic nonlinear Schrödinger equation, vortex solitons were first introduced by V. L. Ginzburg and L. P. Pitaevski, “On the theory of superfluidity,” Sov. Phys. JETP 7, 858–861 (1959) [Zh. Eksp. Teor. Fiz. 34, 1240–1245 (1958)]; see also L. P. Pitaevski, “Vortex lines in an imperfect Bose gas,” Sov. Phys. JETP 13, 451–454 (1961) [Zh. Eksp. Teor. Fiz. 40, 646–651 (1961)], on topological excitations in superfluids. The term vortex had been used much earlier for different (linear) physical processes and for different defining equations.

Yu. S. Kivshar, V. V. Afanasjev, and A. W. Snyder, “Dark-like bright solitons,” Opt. Commun. 126, 348–356 (1996).

[CrossRef]

D. E. Pelinovsky, Yu. S. Kivshar, and V. V. Afanasjev, “Instability-induced dynamics of dark solitons,” Phys. Rev. E 53, 2015–2032 (1996).

[CrossRef]

D. E. Pelinovsky, V. V. Afanasjev, and Yu. S. Kivshar, “Nonlinear theory of oscillating, decaying, and collapsing solitons in the generalized nonlinear Schrödinger equation,” Phys. Rev. E 52, 1940–1953 (1996).

[CrossRef]

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, “Observation of Manakov spatial solitons in AlGaAs planar waveguides,” Phys. Rev. Lett. 76, 3699–3702 (1996).

[CrossRef]
[PubMed]

S. A. Akhmanov, A. P. Sukhorukov, and R. V. Khokhlov, “Self-focusing and self-trapping of intense light beams in a nonlinear medium,” Sov. Phys. JETP 23, 1025–1033 (1966) [Zh. Eksp. Teor. Fiz. 50, 1537–1549 (1966)].

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, “Observation of Manakov spatial solitons in AlGaAs planar waveguides,” Phys. Rev. Lett. 76, 3699–3702 (1996).

[CrossRef]
[PubMed]

N. N. Akhmediev, V. M. Eleonsky, N. E. Kulagin, and L. P. Shil’nikov, “Steady-state pulses in a birefringent nonlinear optical fibers: soliton multiplication process,” Pis’ma Zh. Tekh. Fiz. 15, 19–23 (1989) [Sov. Tech. Phys. Lett. 15, 587–588 (1989)]; M. Haelterman and A. P. Sheppard, “Bifurcation phenomena and multiple soliton-bound states in isotropic Kerr media,” Phys. Rev. E 49, 3376–3381 (1994).

[CrossRef]

The use of the nonlinearity-induced refractive-index change created by an intense beam for guiding particles (electrons and atoms) was suggested even earlier; see G. A. Askar’yan, “Effect of the gradient of a strong electromagnetic beam on electrons and atoms,” Sov. Phys. JETP 15, 1088–1090 (1962) [Zh. Eksp. Teor. Fiz. 42, 1567–1570 (1962)].

M. Shalaby and A. J. Barthelemy, “Observation of the self-guided propagation of a dark and bright spatial soliton pair in a focusing nonlinear medium,” IEEE J. Quantum Electron. 28, 2736–2741 (1992).

[CrossRef]

A. L. Berkhoer and V. E. Zakharov, “Self-excitation of waves with different polarizations in nonlinear media,” Sov. Phys. JETP 31, 486–493 (1970) [Zh. Eksp. Teor. Fiz. 58, 903–911 (1970)].

A. V. Buryak, Yu. S. Kivshar, and D. F. Parker, “Coupling between bright and dark solitons,” Phys. Lett. A 215, 57–62 (1996).

[CrossRef]

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, “Stability of three-wave parametric solitons in diffractive quadratic media,” Phys. Rev. Lett. 77, 5210–5213 (1996); A. V. Buryak and Yu. S. Kivshar, “Multistability of three-wave parametric self-trapping,” Phys. Rev. Lett. 78, 3286–3289 (1997); C. Etrich, U. Peschel, F. Lederer, and B. A. Malomed, “Stability of temporal chirped solitary waves in quadratically nonlinear media,” Phys. Rev. E 55, 6155–6161 (1997).

[CrossRef]
[PubMed]

A. W. Snyder, D. J. Mitchell, and A. V. Buryak, “Qualitative theory of bright solitons—the soliton sketch,” J. Opt. Soc. Am. B 13, 1146–1150 (1996).

[CrossRef]

D. E. Pelinovsky, A. V. Buryak, and Yu. S. Kivshar, “Instability of solitons governed by quadratic nonlinearities,” Phys. Rev. Lett. 75, 591–595 (1995).

[CrossRef]
[PubMed]

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–480 (1964).

[CrossRef]

D. N. Christodoulides and R. I. Joseph, “Vector solitons in birefringent nonlinear dispersive media,” Opt. Lett. 13, 53–55 (1988); M. V. Tratnik and J. E. Sipe, “Bound solitary waves in a birefringent optical fiber,” Phys. Rev. A 38, 2011–2017 (1988); S. Trillo, S. Wabnitz, E. M. Wright, and G. Stegeman, “Optical solitary waves induced by cross-phase modulation,” Opt. Lett. 13, 871–873 (1988).

[CrossRef]
[PubMed]

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three-dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76, 2698–2701 (1996).

[CrossRef]
[PubMed]

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Spiraling bright spatial solitons formed by the breakup of an optical vortex in a saturable self-focusing medium,” J. Opt. Soc. Am. B 12, 2046–2052 (1995).

[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994); M. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salamo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons,” Opt. Lett. 21, 324–326 (1996).

[CrossRef]
[PubMed]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping in an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).

[CrossRef]
[PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).

[CrossRef]
[PubMed]

See, e.g., J. H. Marburger and E. L. Dawes, “Dynamic formation of a small-scale filament,” Phys. Rev. Lett. 21, 556–558 (1968); E. L. Dawes and J. H. Marburger, “Computer studies in self-focusing,” Phys. Rev. 179, 862–868 (1969).

[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994); M. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salamo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons,” Opt. Lett. 21, 324–326 (1996).

[CrossRef]
[PubMed]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping in an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).

[CrossRef]
[PubMed]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping in an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).

[CrossRef]
[PubMed]

N. N. Akhmediev, V. M. Eleonsky, N. E. Kulagin, and L. P. Shil’nikov, “Steady-state pulses in a birefringent nonlinear optical fibers: soliton multiplication process,” Pis’ma Zh. Tekh. Fiz. 15, 19–23 (1989) [Sov. Tech. Phys. Lett. 15, 587–588 (1989)]; M. Haelterman and A. P. Sheppard, “Bifurcation phenomena and multiple soliton-bound states in isotropic Kerr media,” Phys. Rev. E 49, 3376–3381 (1994).

[CrossRef]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).

[CrossRef]
[PubMed]

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–480 (1964).

[CrossRef]

As spatially localized solutions of the defocusing cubic nonlinear Schrödinger equation, vortex solitons were first introduced by V. L. Ginzburg and L. P. Pitaevski, “On the theory of superfluidity,” Sov. Phys. JETP 7, 858–861 (1959) [Zh. Eksp. Teor. Fiz. 34, 1240–1245 (1958)]; see also L. P. Pitaevski, “Vortex lines in an imperfect Bose gas,” Sov. Phys. JETP 13, 451–454 (1961) [Zh. Eksp. Teor. Fiz. 40, 646–651 (1961)], on topological excitations in superfluids. The term vortex had been used much earlier for different (linear) physical processes and for different defining equations.

A. W. Snyder, D. J. Mitchell, and M. Haelterman, “Parallel spatial solitons,” Opt. Commun. 116, 365–368 (1995).

[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).

[CrossRef]
[PubMed]

P. K. Kaw, K. Nishikawa, Y. Yoshida, and A. Hasegawa, “Two-dimensional and three-dimensional envelope solitons,” Phys. Rev. Lett. 35, 88–91 (1975); J. Z. Wilcox and T. J. Wilcox, “Stability of localized plasma model in two and three dimensions,” Phys. Rev. Lett. 34, 1160–1163 (1975).

[CrossRef]

A. W. Snyder, S. Hewlett, and D. J. Mitchell, “Periodic solitons in optics,” Phys. Rev. E 51, 6297–6300 (1995).

[CrossRef]

A. W. Snyder, S. Hewlett, and D. J. Mitchell, “Dynamic spatial solitons,” Phys. Rev. Lett. 72, 1012–1016 (1994).

[CrossRef]
[PubMed]

M. D. Iturbe-Castillo, P. A. Marquez Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).

[CrossRef]

C. K. R. T. Jones and J. Moloney, “Instability of standing waves in nonlinear optical waveguides,” Phys. Lett. A 117, 175–180 (1986).

[CrossRef]

D. N. Christodoulides and R. I. Joseph, “Vector solitons in birefringent nonlinear dispersive media,” Opt. Lett. 13, 53–55 (1988); M. V. Tratnik and J. E. Sipe, “Bound solitary waves in a birefringent optical fiber,” Phys. Rev. A 38, 2011–2017 (1988); S. Trillo, S. Wabnitz, E. M. Wright, and G. Stegeman, “Optical solitary waves induced by cross-phase modulation,” Opt. Lett. 13, 871–873 (1988).

[CrossRef]
[PubMed]

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, “Observation of Manakov spatial solitons in AlGaAs planar waveguides,” Phys. Rev. Lett. 76, 3699–3702 (1996).

[CrossRef]
[PubMed]

Yu. N. Karamzin and A. P. Sukhorukov, “Mutual focusing of high-power light beams in media with quadratic nonlinearity,” Zh. Eksp. Teor. Fiz. 68, 834–847 (1975) [Sov. Phys. JETP 41, 414–420 (1976)]; A. V. Buryak and Yu. S. Kivshar, “Spatial optical solitons governed by quadratic nonlinearity,” Opt. Lett. 19, 1612–1614 (1994); L. Torner, C. R. Menyuk, and G. I. Stegeman, “Excitation of solitons with cascaded χ(2) nonlinearity,” Opt. Lett. 19, 1615–1617 (1994).

[CrossRef]
[PubMed]

P. K. Kaw, K. Nishikawa, Y. Yoshida, and A. Hasegawa, “Two-dimensional and three-dimensional envelope solitons,” Phys. Rev. Lett. 35, 88–91 (1975); J. Z. Wilcox and T. J. Wilcox, “Stability of localized plasma model in two and three dimensions,” Phys. Rev. Lett. 34, 1160–1163 (1975).

[CrossRef]

J. B. Keller, “The geometrical theory of diffraction,” J. Opt. Soc. Am. 12, 116–130 (1962).

[CrossRef]

P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15, 1005–1008 (1965).

[CrossRef]

S. A. Akhmanov, A. P. Sukhorukov, and R. V. Khokhlov, “Self-focusing and self-trapping of intense light beams in a nonlinear medium,” Sov. Phys. JETP 23, 1025–1033 (1966) [Zh. Eksp. Teor. Fiz. 50, 1537–1549 (1966)].

D. E. Pelinovsky, Yu. S. Kivshar, and V. V. Afanasjev, “Instability-induced dynamics of dark solitons,” Phys. Rev. E 53, 2015–2032 (1996).

[CrossRef]

Yu. S. Kivshar, V. V. Afanasjev, and A. W. Snyder, “Dark-like bright solitons,” Opt. Commun. 126, 348–356 (1996).

[CrossRef]

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, “Stability of three-wave parametric solitons in diffractive quadratic media,” Phys. Rev. Lett. 77, 5210–5213 (1996); A. V. Buryak and Yu. S. Kivshar, “Multistability of three-wave parametric self-trapping,” Phys. Rev. Lett. 78, 3286–3289 (1997); C. Etrich, U. Peschel, F. Lederer, and B. A. Malomed, “Stability of temporal chirped solitary waves in quadratically nonlinear media,” Phys. Rev. E 55, 6155–6161 (1997).

[CrossRef]
[PubMed]

A. V. Buryak, Yu. S. Kivshar, and D. F. Parker, “Coupling between bright and dark solitons,” Phys. Lett. A 215, 57–62 (1996).

[CrossRef]

D. E. Pelinovsky, V. V. Afanasjev, and Yu. S. Kivshar, “Nonlinear theory of oscillating, decaying, and collapsing solitons in the generalized nonlinear Schrödinger equation,” Phys. Rev. E 52, 1940–1953 (1996).

[CrossRef]

D. E. Pelinovsky, A. V. Buryak, and Yu. S. Kivshar, “Instability of solitons governed by quadratic nonlinearities,” Phys. Rev. Lett. 75, 591–595 (1995).

[CrossRef]
[PubMed]

A. W. Snyder, D. J. Mitchell, and Yu. S. Kivshar, “Unification of linear and nonlinear guided wave optics,” Mod. Phys. Lett. B 9, 1479–1506 (1995).

[CrossRef]

A. W. Snyder, D. J. Mitchell, and Yu. S. Kivshar, “Linear perspective of solitons,” in Physics and Applications of Optical Solitons in Fibers, A. Hasegawa, ed. (Kluwer Academic, Amsterdam, 1996), pp. 263–275.

Yu. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. (to be published).

M. G. Vakhitov and A. A. Kolokolov, “Stationary solutions of the wave equation in a medium with nonlinearity saturation,” Radiophys. Quantum Electron. 16, 783–789 (1973); applies only for a Kerr medium and no waveguide structures.

[CrossRef]

N. N. Akhmediev, V. M. Eleonsky, N. E. Kulagin, and L. P. Shil’nikov, “Steady-state pulses in a birefringent nonlinear optical fibers: soliton multiplication process,” Pis’ma Zh. Tekh. Fiz. 15, 19–23 (1989) [Sov. Tech. Phys. Lett. 15, 587–588 (1989)]; M. Haelterman and A. P. Sheppard, “Bifurcation phenomena and multiple soliton-bound states in isotropic Kerr media,” Phys. Rev. E 49, 3376–3381 (1994).

[CrossRef]

A. W. Snyder, D. J. Mitchell, and F. Ladouceur, “Self-induced optical fibers: spatial solitary waves,” Opt. Lett. 10, 21–23 (1991).

[CrossRef]

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1985).

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three-dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76, 2698–2701 (1996).

[CrossRef]
[PubMed]

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Spiraling bright spatial solitons formed by the breakup of an optical vortex in a saturable self-focusing medium,” J. Opt. Soc. Am. B 12, 2046–2052 (1995).

[CrossRef]

Yu. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. (to be published).

S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Sov. Phys. JETP 38, 248–253 (1974) [Zh. Eksp. Teor. Fiz. 65, 505–516 (1973)].

See, e.g., J. H. Marburger and E. L. Dawes, “Dynamic formation of a small-scale filament,” Phys. Rev. Lett. 21, 556–558 (1968); E. L. Dawes and J. H. Marburger, “Computer studies in self-focusing,” Phys. Rev. 179, 862–868 (1969).

[CrossRef]

M. D. Iturbe-Castillo, P. A. Marquez Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).

[CrossRef]

L. Torner, C. R. Menyuk, W. E. Torruellas, and G. I. Stegeman, “Two-dimensional solitons with second-harmonic nonlinearity,” Opt. Lett. 20, 13–15 (1995); A. V. Buryak, Yu. S. Kivshar, and V. V. Steblina, “Self-trapping of light beams and parametric solitons in diffractive quadratic media,” Phys. Rev. A 52, 1670–1674 (1995).

[CrossRef]
[PubMed]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).

[CrossRef]
[PubMed]

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538–1541 (1997).

[CrossRef]

A. W. Snyder and D. J. Mitchell, “Mighty morphing spatial solitons and bullets,” Opt. Lett. 22, 16–18 (1997).

[CrossRef]
[PubMed]

A. W. Snyder, D. J. Mitchell, and A. V. Buryak, “Qualitative theory of bright solitons—the soliton sketch,” J. Opt. Soc. Am. B 13, 1146–1150 (1996).

[CrossRef]

D. J. Mitchell, A. W. Snyder, and L. Poladian, “Interacting self-guided beams viewed as particles: Lorentz force derivation,” Phys. Rev. Lett. 77, 271–273 (1996).

[CrossRef]
[PubMed]

A. W. Snyder, S. Hewlett, and D. J. Mitchell, “Periodic solitons in optics,” Phys. Rev. E 51, 6297–6300 (1995).

[CrossRef]

A. W. Snyder, D. J. Mitchell, and M. Haelterman, “Parallel spatial solitons,” Opt. Commun. 116, 365–368 (1995).

[CrossRef]

A. W. Snyder, D. J. Mitchell, and Yu. S. Kivshar, “Unification of linear and nonlinear guided wave optics,” Mod. Phys. Lett. B 9, 1479–1506 (1995).

[CrossRef]

A. W. Snyder, S. Hewlett, and D. J. Mitchell, “Dynamic spatial solitons,” Phys. Rev. Lett. 72, 1012–1016 (1994).

[CrossRef]
[PubMed]

D. J. Mitchell and A. W. Snyder, “Stability of fundamental nonlinear guided waves,” J. Opt. Soc. Am. B 10, 1572–1580 (1993); applicable to all nonlinearities and also in the presence of waveguide structures.

[CrossRef]

In a defocusing Kerr medium, the only known stable soliton is “a black spatial soliton of circular cross section” (sometimes called a vortex soliton; see Ref. 10), first predicted in optics in the paper by A. W. Snyder, L. Poladian, and D. J. Mitchell, “Stable black self-guided beams of circular symmetry in a bulk Kerr medium,” Opt. Lett. 17, 789–791 (1992). This letter is also the first to suggest such solitons as suitable for guiding signals.

[CrossRef]
[PubMed]

L. Poladian, A. W. Snyder, and D. J. Mitchell, “Spiralling spatial solitons,” Opt. Commun. 85, 59–62 (1991).

[CrossRef]

D. J. Mitchell, A. W. Snyder, and L. Poladian, “Self-guided beam interaction: method of invariants,” Electron. Lett. 27, 848–849 (1991).

[CrossRef]

A. W. Snyder, D. J. Mitchell, and F. Ladouceur, “Self-induced optical fibers: spatial solitary waves,” Opt. Lett. 10, 21–23 (1991).

[CrossRef]

A. W. Snyder, D. J. Mitchell, and Yu. S. Kivshar, “Linear perspective of solitons,” in Physics and Applications of Optical Solitons in Fibers, A. Hasegawa, ed. (Kluwer Academic, Amsterdam, 1996), pp. 263–275.

C. K. R. T. Jones and J. Moloney, “Instability of standing waves in nonlinear optical waveguides,” Phys. Lett. A 117, 175–180 (1986).

[CrossRef]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping in an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).

[CrossRef]
[PubMed]

P. K. Kaw, K. Nishikawa, Y. Yoshida, and A. Hasegawa, “Two-dimensional and three-dimensional envelope solitons,” Phys. Rev. Lett. 35, 88–91 (1975); J. Z. Wilcox and T. J. Wilcox, “Stability of localized plasma model in two and three dimensions,” Phys. Rev. Lett. 34, 1160–1163 (1975).

[CrossRef]

A. V. Buryak, Yu. S. Kivshar, and D. F. Parker, “Coupling between bright and dark solitons,” Phys. Lett. A 215, 57–62 (1996).

[CrossRef]

D. E. Pelinovsky, V. V. Afanasjev, and Yu. S. Kivshar, “Nonlinear theory of oscillating, decaying, and collapsing solitons in the generalized nonlinear Schrödinger equation,” Phys. Rev. E 52, 1940–1953 (1996).

[CrossRef]

D. E. Pelinovsky, Yu. S. Kivshar, and V. V. Afanasjev, “Instability-induced dynamics of dark solitons,” Phys. Rev. E 53, 2015–2032 (1996).

[CrossRef]

D. E. Pelinovsky, A. V. Buryak, and Yu. S. Kivshar, “Instability of solitons governed by quadratic nonlinearities,” Phys. Rev. Lett. 75, 591–595 (1995).

[CrossRef]
[PubMed]

As spatially localized solutions of the defocusing cubic nonlinear Schrödinger equation, vortex solitons were first introduced by V. L. Ginzburg and L. P. Pitaevski, “On the theory of superfluidity,” Sov. Phys. JETP 7, 858–861 (1959) [Zh. Eksp. Teor. Fiz. 34, 1240–1245 (1958)]; see also L. P. Pitaevski, “Vortex lines in an imperfect Bose gas,” Sov. Phys. JETP 13, 451–454 (1961) [Zh. Eksp. Teor. Fiz. 40, 646–651 (1961)], on topological excitations in superfluids. The term vortex had been used much earlier for different (linear) physical processes and for different defining equations.

D. J. Mitchell, A. W. Snyder, and L. Poladian, “Interacting self-guided beams viewed as particles: Lorentz force derivation,” Phys. Rev. Lett. 77, 271–273 (1996).

[CrossRef]
[PubMed]

In a defocusing Kerr medium, the only known stable soliton is “a black spatial soliton of circular cross section” (sometimes called a vortex soliton; see Ref. 10), first predicted in optics in the paper by A. W. Snyder, L. Poladian, and D. J. Mitchell, “Stable black self-guided beams of circular symmetry in a bulk Kerr medium,” Opt. Lett. 17, 789–791 (1992). This letter is also the first to suggest such solitons as suitable for guiding signals.

[CrossRef]
[PubMed]

D. J. Mitchell, A. W. Snyder, and L. Poladian, “Self-guided beam interaction: method of invariants,” Electron. Lett. 27, 848–849 (1991).

[CrossRef]

L. Poladian, A. W. Snyder, and D. J. Mitchell, “Spiralling spatial solitons,” Opt. Commun. 85, 59–62 (1991).

[CrossRef]

M. Shih, M. Segev, and G. Salamo, “Three-dimensional spiralling of interacting spatial solitons,” Phys. Rev. Lett. 78, 2551–2554 (1997).

[CrossRef]

M. Shih, M. Segev, and G. Salamo, “Circular waveguides induced by two-dimensional bright steady-state photorefractive screening solitons,” Opt. Lett. 21, 931–933 (1996).

[CrossRef]
[PubMed]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping in an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).

[CrossRef]
[PubMed]

M. D. Iturbe-Castillo, P. A. Marquez Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).

[CrossRef]

M. Shih, M. Segev, and G. Salamo, “Three-dimensional spiralling of interacting spatial solitons,” Phys. Rev. Lett. 78, 2551–2554 (1997).

[CrossRef]

M. Shih and M. Segev, “Incoherent collision between two-dimensional bright steady-state photorefractive spatial screening solitons,” Opt. Lett. 21, 1538–1540 (1996).

[CrossRef]
[PubMed]

M. Shih, M. Segev, and G. Salamo, “Circular waveguides induced by two-dimensional bright steady-state photorefractive screening solitons,” Opt. Lett. 21, 931–933 (1996).

[CrossRef]
[PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994); M. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salamo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons,” Opt. Lett. 21, 324–326 (1996).

[CrossRef]
[PubMed]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping in an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).

[CrossRef]
[PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).

[CrossRef]
[PubMed]

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Zh. Eksp. Teor. Fiz. 61, 118–134 (1971) [Sov. Phys. JETP 34, 62–69 (1972)].

M. Shalaby and A. J. Barthelemy, “Observation of the self-guided propagation of a dark and bright spatial soliton pair in a focusing nonlinear medium,” IEEE J. Quantum Electron. 28, 2736–2741 (1992).

[CrossRef]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping in an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).

[CrossRef]
[PubMed]

M. Shih, M. Segev, and G. Salamo, “Three-dimensional spiralling of interacting spatial solitons,” Phys. Rev. Lett. 78, 2551–2554 (1997).

[CrossRef]

M. Shih, M. Segev, and G. Salamo, “Circular waveguides induced by two-dimensional bright steady-state photorefractive screening solitons,” Opt. Lett. 21, 931–933 (1996).

[CrossRef]
[PubMed]

M. Shih and M. Segev, “Incoherent collision between two-dimensional bright steady-state photorefractive spatial screening solitons,” Opt. Lett. 21, 1538–1540 (1996).

[CrossRef]
[PubMed]

N. N. Akhmediev, V. M. Eleonsky, N. E. Kulagin, and L. P. Shil’nikov, “Steady-state pulses in a birefringent nonlinear optical fibers: soliton multiplication process,” Pis’ma Zh. Tekh. Fiz. 15, 19–23 (1989) [Sov. Tech. Phys. Lett. 15, 587–588 (1989)]; M. Haelterman and A. P. Sheppard, “Bifurcation phenomena and multiple soliton-bound states in isotropic Kerr media,” Phys. Rev. E 49, 3376–3381 (1994).

[CrossRef]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping in an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).

[CrossRef]
[PubMed]

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538–1541 (1997).

[CrossRef]

A. W. Snyder and D. J. Mitchell, “Mighty morphing spatial solitons and bullets,” Opt. Lett. 22, 16–18 (1997).

[CrossRef]
[PubMed]

Yu. S. Kivshar, V. V. Afanasjev, and A. W. Snyder, “Dark-like bright solitons,” Opt. Commun. 126, 348–356 (1996).

[CrossRef]

A. W. Snyder, D. J. Mitchell, and A. V. Buryak, “Qualitative theory of bright solitons—the soliton sketch,” J. Opt. Soc. Am. B 13, 1146–1150 (1996).

[CrossRef]

A. W. Snyder, “The linear perspective to soliton dynamics,” Opt. Photonics News 7(12), 27–28 (1996).

[CrossRef]

D. J. Mitchell, A. W. Snyder, and L. Poladian, “Interacting self-guided beams viewed as particles: Lorentz force derivation,” Phys. Rev. Lett. 77, 271–273 (1996).

[CrossRef]
[PubMed]

A. W. Snyder, D. J. Mitchell, and M. Haelterman, “Parallel spatial solitons,” Opt. Commun. 116, 365–368 (1995).

[CrossRef]

A. W. Snyder, S. Hewlett, and D. J. Mitchell, “Periodic solitons in optics,” Phys. Rev. E 51, 6297–6300 (1995).

[CrossRef]

A. W. Snyder, D. J. Mitchell, and Yu. S. Kivshar, “Unification of linear and nonlinear guided wave optics,” Mod. Phys. Lett. B 9, 1479–1506 (1995).

[CrossRef]

A. W. Snyder, S. Hewlett, and D. J. Mitchell, “Dynamic spatial solitons,” Phys. Rev. Lett. 72, 1012–1016 (1994).

[CrossRef]
[PubMed]

A. W. Snyder and A. P. Sheppard, “Collisons, steering and guidance with spatial solitons,” Opt. Lett. 18, 482–484 (1993).

[CrossRef]
[PubMed]

D. J. Mitchell and A. W. Snyder, “Stability of fundamental nonlinear guided waves,” J. Opt. Soc. Am. B 10, 1572–1580 (1993); applicable to all nonlinearities and also in the presence of waveguide structures.

[CrossRef]

In a defocusing Kerr medium, the only known stable soliton is “a black spatial soliton of circular cross section” (sometimes called a vortex soliton; see Ref. 10), first predicted in optics in the paper by A. W. Snyder, L. Poladian, and D. J. Mitchell, “Stable black self-guided beams of circular symmetry in a bulk Kerr medium,” Opt. Lett. 17, 789–791 (1992). This letter is also the first to suggest such solitons as suitable for guiding signals.

[CrossRef]
[PubMed]

L. Poladian, A. W. Snyder, and D. J. Mitchell, “Spiralling spatial solitons,” Opt. Commun. 85, 59–62 (1991).

[CrossRef]

D. J. Mitchell, A. W. Snyder, and L. Poladian, “Self-guided beam interaction: method of invariants,” Electron. Lett. 27, 848–849 (1991).

[CrossRef]

A. W. Snyder, D. J. Mitchell, and F. Ladouceur, “Self-induced optical fibers: spatial solitary waves,” Opt. Lett. 10, 21–23 (1991).

[CrossRef]

A. W. Snyder, D. J. Mitchell, and Yu. S. Kivshar, “Linear perspective of solitons,” in Physics and Applications of Optical Solitons in Fibers, A. Hasegawa, ed. (Kluwer Academic, Amsterdam, 1996), pp. 263–275.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1985).

For the most recent overview of the experimental observations of spatial optical solitons, see the paper by G. I. Stegeman, “The growing family of spatial solitons,” Opt. Appl. 26, 240–248 (1996).

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, “Observation of Manakov spatial solitons in AlGaAs planar waveguides,” Phys. Rev. Lett. 76, 3699–3702 (1996).

[CrossRef]
[PubMed]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).

[CrossRef]
[PubMed]

L. Torner, C. R. Menyuk, W. E. Torruellas, and G. I. Stegeman, “Two-dimensional solitons with second-harmonic nonlinearity,” Opt. Lett. 20, 13–15 (1995); A. V. Buryak, Yu. S. Kivshar, and V. V. Steblina, “Self-trapping of light beams and parametric solitons in diffractive quadratic media,” Phys. Rev. A 52, 1670–1674 (1995).

[CrossRef]
[PubMed]

M. D. Iturbe-Castillo, P. A. Marquez Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).

[CrossRef]

Yu. N. Karamzin and A. P. Sukhorukov, “Mutual focusing of high-power light beams in media with quadratic nonlinearity,” Zh. Eksp. Teor. Fiz. 68, 834–847 (1975) [Sov. Phys. JETP 41, 414–420 (1976)]; A. V. Buryak and Yu. S. Kivshar, “Spatial optical solitons governed by quadratic nonlinearity,” Opt. Lett. 19, 1612–1614 (1994); L. Torner, C. R. Menyuk, and G. I. Stegeman, “Excitation of solitons with cascaded χ(2) nonlinearity,” Opt. Lett. 19, 1615–1617 (1994).

[CrossRef]
[PubMed]

S. A. Akhmanov, A. P. Sukhorukov, and R. V. Khokhlov, “Self-focusing and self-trapping of intense light beams in a nonlinear medium,” Sov. Phys. JETP 23, 1025–1033 (1966) [Zh. Eksp. Teor. Fiz. 50, 1537–1549 (1966)].

T. Thwaites, “Will optical fibres become obsolete?” New Scientist, January12, 1991, p. 14.

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three-dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76, 2698–2701 (1996).

[CrossRef]
[PubMed]

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Spiraling bright spatial solitons formed by the breakup of an optical vortex in a saturable self-focusing medium,” J. Opt. Soc. Am. B 12, 2046–2052 (1995).

[CrossRef]

V. Tikhonenko, Laser Physics Centre, Australian National University, ACT 0200 Canberra, Australia (personal communication, 1997).

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).

[CrossRef]
[PubMed]

L. Torner, C. R. Menyuk, W. E. Torruellas, and G. I. Stegeman, “Two-dimensional solitons with second-harmonic nonlinearity,” Opt. Lett. 20, 13–15 (1995); A. V. Buryak, Yu. S. Kivshar, and V. V. Steblina, “Self-trapping of light beams and parametric solitons in diffractive quadratic media,” Phys. Rev. A 52, 1670–1674 (1995).

[CrossRef]
[PubMed]

L. Torner, C. R. Menyuk, W. E. Torruellas, and G. I. Stegeman, “Two-dimensional solitons with second-harmonic nonlinearity,” Opt. Lett. 20, 13–15 (1995); A. V. Buryak, Yu. S. Kivshar, and V. V. Steblina, “Self-trapping of light beams and parametric solitons in diffractive quadratic media,” Phys. Rev. A 52, 1670–1674 (1995).

[CrossRef]
[PubMed]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).

[CrossRef]
[PubMed]

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–480 (1964).

[CrossRef]

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, “Stability of three-wave parametric solitons in diffractive quadratic media,” Phys. Rev. Lett. 77, 5210–5213 (1996); A. V. Buryak and Yu. S. Kivshar, “Multistability of three-wave parametric self-trapping,” Phys. Rev. Lett. 78, 3286–3289 (1997); C. Etrich, U. Peschel, F. Lederer, and B. A. Malomed, “Stability of temporal chirped solitary waves in quadratically nonlinear media,” Phys. Rev. E 55, 6155–6161 (1997).

[CrossRef]
[PubMed]

M. G. Vakhitov and A. A. Kolokolov, “Stationary solutions of the wave equation in a medium with nonlinearity saturation,” Radiophys. Quantum Electron. 16, 783–789 (1973); applies only for a Kerr medium and no waveguide structures.

[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994); M. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salamo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons,” Opt. Lett. 21, 324–326 (1996).

[CrossRef]
[PubMed]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).

[CrossRef]
[PubMed]

M. D. Iturbe-Castillo, P. A. Marquez Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).

[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).

[CrossRef]
[PubMed]

M. I. Weinstein, “Lyapunov stability of ground state of nonlinear evolution equations,” SIAM J. Math. Anal. 16, 472–483 (1985).

[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994); M. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salamo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons,” Opt. Lett. 21, 324–326 (1996).

[CrossRef]
[PubMed]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping in an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).

[CrossRef]
[PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).

[CrossRef]
[PubMed]

P. K. Kaw, K. Nishikawa, Y. Yoshida, and A. Hasegawa, “Two-dimensional and three-dimensional envelope solitons,” Phys. Rev. Lett. 35, 88–91 (1975); J. Z. Wilcox and T. J. Wilcox, “Stability of localized plasma model in two and three dimensions,” Phys. Rev. Lett. 34, 1160–1163 (1975).

[CrossRef]

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Zh. Eksp. Teor. Fiz. 61, 118–134 (1971) [Sov. Phys. JETP 34, 62–69 (1972)].

A. L. Berkhoer and V. E. Zakharov, “Self-excitation of waves with different polarizations in nonlinear media,” Sov. Phys. JETP 31, 486–493 (1970) [Zh. Eksp. Teor. Fiz. 58, 903–911 (1970)].

M. D. Iturbe-Castillo, P. A. Marquez Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).

[CrossRef]

D. J. Mitchell, A. W. Snyder, and L. Poladian, “Self-guided beam interaction: method of invariants,” Electron. Lett. 27, 848–849 (1991).

[CrossRef]

M. Shalaby and A. J. Barthelemy, “Observation of the self-guided propagation of a dark and bright spatial soliton pair in a focusing nonlinear medium,” IEEE J. Quantum Electron. 28, 2736–2741 (1992).

[CrossRef]

J. B. Keller, “The geometrical theory of diffraction,” J. Opt. Soc. Am. 12, 116–130 (1962).

[CrossRef]

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Spiraling bright spatial solitons formed by the breakup of an optical vortex in a saturable self-focusing medium,” J. Opt. Soc. Am. B 12, 2046–2052 (1995).

[CrossRef]

D. J. Mitchell and A. W. Snyder, “Stability of fundamental nonlinear guided waves,” J. Opt. Soc. Am. B 10, 1572–1580 (1993); applicable to all nonlinearities and also in the presence of waveguide structures.

[CrossRef]

A. W. Snyder, D. J. Mitchell, and A. V. Buryak, “Qualitative theory of bright solitons—the soliton sketch,” J. Opt. Soc. Am. B 13, 1146–1150 (1996).

[CrossRef]

A. W. Snyder, D. J. Mitchell, and Yu. S. Kivshar, “Unification of linear and nonlinear guided wave optics,” Mod. Phys. Lett. B 9, 1479–1506 (1995).

[CrossRef]

T. Thwaites, “Will optical fibres become obsolete?” New Scientist, January12, 1991, p. 14.

For the most recent overview of the experimental observations of spatial optical solitons, see the paper by G. I. Stegeman, “The growing family of spatial solitons,” Opt. Appl. 26, 240–248 (1996).

L. Poladian, A. W. Snyder, and D. J. Mitchell, “Spiralling spatial solitons,” Opt. Commun. 85, 59–62 (1991).

[CrossRef]

A. W. Snyder, D. J. Mitchell, and M. Haelterman, “Parallel spatial solitons,” Opt. Commun. 116, 365–368 (1995).

[CrossRef]

Yu. S. Kivshar, V. V. Afanasjev, and A. W. Snyder, “Dark-like bright solitons,” Opt. Commun. 126, 348–356 (1996).

[CrossRef]

D. Hart and E. M. Wright, “Stability of the TE0 guided wave of a nonlinear waveguide with a self-defocusing bounding medium,” Opt. Lett. 17, 121–123 (1992).

[CrossRef]
[PubMed]

L. Torner, C. R. Menyuk, W. E. Torruellas, and G. I. Stegeman, “Two-dimensional solitons with second-harmonic nonlinearity,” Opt. Lett. 20, 13–15 (1995); A. V. Buryak, Yu. S. Kivshar, and V. V. Steblina, “Self-trapping of light beams and parametric solitons in diffractive quadratic media,” Phys. Rev. A 52, 1670–1674 (1995).

[CrossRef]
[PubMed]

D. N. Christodoulides and R. I. Joseph, “Vector solitons in birefringent nonlinear dispersive media,” Opt. Lett. 13, 53–55 (1988); M. V. Tratnik and J. E. Sipe, “Bound solitary waves in a birefringent optical fiber,” Phys. Rev. A 38, 2011–2017 (1988); S. Trillo, S. Wabnitz, E. M. Wright, and G. Stegeman, “Optical solitary waves induced by cross-phase modulation,” Opt. Lett. 13, 871–873 (1988).

[CrossRef]
[PubMed]

M. Shih, M. Segev, and G. Salamo, “Circular waveguides induced by two-dimensional bright steady-state photorefractive screening solitons,” Opt. Lett. 21, 931–933 (1996).

[CrossRef]
[PubMed]

M. Shih and M. Segev, “Incoherent collision between two-dimensional bright steady-state photorefractive spatial screening solitons,” Opt. Lett. 21, 1538–1540 (1996).

[CrossRef]
[PubMed]

W. Krolikowski and S. A. Holmstrom, “Fusion and birth of spatial solitons upon collision,” Opt. Lett. 22, 369–371 (1997).

[CrossRef]
[PubMed]

A. W. Snyder and D. J. Mitchell, “Mighty morphing spatial solitons and bullets,” Opt. Lett. 22, 16–18 (1997).

[CrossRef]
[PubMed]

J. T. Manassah, “Induced waveguiding effects in a two-dimensional nonlinear medium,” Opt. Lett. 16, 587–589 (1991).

[CrossRef]
[PubMed]

A. W. Snyder, D. J. Mitchell, and F. Ladouceur, “Self-induced optical fibers: spatial solitary waves,” Opt. Lett. 10, 21–23 (1991).

[CrossRef]

A. W. Snyder and A. P. Sheppard, “Collisons, steering and guidance with spatial solitons,” Opt. Lett. 18, 482–484 (1993).

[CrossRef]
[PubMed]

In a defocusing Kerr medium, the only known stable soliton is “a black spatial soliton of circular cross section” (sometimes called a vortex soliton; see Ref. 10), first predicted in optics in the paper by A. W. Snyder, L. Poladian, and D. J. Mitchell, “Stable black self-guided beams of circular symmetry in a bulk Kerr medium,” Opt. Lett. 17, 789–791 (1992). This letter is also the first to suggest such solitons as suitable for guiding signals.

[CrossRef]
[PubMed]

A. W. Snyder, “The linear perspective to soliton dynamics,” Opt. Photonics News 7(12), 27–28 (1996).

[CrossRef]

A. V. Buryak, Yu. S. Kivshar, and D. F. Parker, “Coupling between bright and dark solitons,” Phys. Lett. A 215, 57–62 (1996).

[CrossRef]

C. K. R. T. Jones and J. Moloney, “Instability of standing waves in nonlinear optical waveguides,” Phys. Lett. A 117, 175–180 (1986).

[CrossRef]

A. W. Snyder, S. Hewlett, and D. J. Mitchell, “Periodic solitons in optics,” Phys. Rev. E 51, 6297–6300 (1995).

[CrossRef]

D. E. Pelinovsky, Yu. S. Kivshar, and V. V. Afanasjev, “Instability-induced dynamics of dark solitons,” Phys. Rev. E 53, 2015–2032 (1996).

[CrossRef]

D. E. Pelinovsky, V. V. Afanasjev, and Yu. S. Kivshar, “Nonlinear theory of oscillating, decaying, and collapsing solitons in the generalized nonlinear Schrödinger equation,” Phys. Rev. E 52, 1940–1953 (1996).

[CrossRef]

D. E. Pelinovsky, A. V. Buryak, and Yu. S. Kivshar, “Instability of solitons governed by quadratic nonlinearities,” Phys. Rev. Lett. 75, 591–595 (1995).

[CrossRef]
[PubMed]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).

[CrossRef]
[PubMed]

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, “Observation of Manakov spatial solitons in AlGaAs planar waveguides,” Phys. Rev. Lett. 76, 3699–3702 (1996).

[CrossRef]
[PubMed]

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, “Stability of three-wave parametric solitons in diffractive quadratic media,” Phys. Rev. Lett. 77, 5210–5213 (1996); A. V. Buryak and Yu. S. Kivshar, “Multistability of three-wave parametric self-trapping,” Phys. Rev. Lett. 78, 3286–3289 (1997); C. Etrich, U. Peschel, F. Lederer, and B. A. Malomed, “Stability of temporal chirped solitary waves in quadratically nonlinear media,” Phys. Rev. E 55, 6155–6161 (1997).

[CrossRef]
[PubMed]

M. Shih, M. Segev, and G. Salamo, “Three-dimensional spiralling of interacting spatial solitons,” Phys. Rev. Lett. 78, 2551–2554 (1997).

[CrossRef]

P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15, 1005–1008 (1965).

[CrossRef]

See, e.g., J. H. Marburger and E. L. Dawes, “Dynamic formation of a small-scale filament,” Phys. Rev. Lett. 21, 556–558 (1968); E. L. Dawes and J. H. Marburger, “Computer studies in self-focusing,” Phys. Rev. 179, 862–868 (1969).

[CrossRef]

P. K. Kaw, K. Nishikawa, Y. Yoshida, and A. Hasegawa, “Two-dimensional and three-dimensional envelope solitons,” Phys. Rev. Lett. 35, 88–91 (1975); J. Z. Wilcox and T. J. Wilcox, “Stability of localized plasma model in two and three dimensions,” Phys. Rev. Lett. 34, 1160–1163 (1975).

[CrossRef]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926 (1992).

[CrossRef]
[PubMed]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping in an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71, 533–536 (1993).

[CrossRef]
[PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994); M. Shih, P. Leach, M. Segev, M. H. Garrett, G. Salamo, and G. C. Valley, “Two-dimensional steady-state photorefractive screening solitons,” Opt. Lett. 21, 324–326 (1996).

[CrossRef]
[PubMed]

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three-dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76, 2698–2701 (1996).

[CrossRef]
[PubMed]

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–480 (1964).

[CrossRef]

A. W. Snyder, S. Hewlett, and D. J. Mitchell, “Dynamic spatial solitons,” Phys. Rev. Lett. 72, 1012–1016 (1994).

[CrossRef]
[PubMed]

D. J. Mitchell, A. W. Snyder, and L. Poladian, “Interacting self-guided beams viewed as particles: Lorentz force derivation,” Phys. Rev. Lett. 77, 271–273 (1996).

[CrossRef]
[PubMed]

N. N. Akhmediev, V. M. Eleonsky, N. E. Kulagin, and L. P. Shil’nikov, “Steady-state pulses in a birefringent nonlinear optical fibers: soliton multiplication process,” Pis’ma Zh. Tekh. Fiz. 15, 19–23 (1989) [Sov. Tech. Phys. Lett. 15, 587–588 (1989)]; M. Haelterman and A. P. Sheppard, “Bifurcation phenomena and multiple soliton-bound states in isotropic Kerr media,” Phys. Rev. E 49, 3376–3381 (1994).

[CrossRef]

M. G. Vakhitov and A. A. Kolokolov, “Stationary solutions of the wave equation in a medium with nonlinearity saturation,” Radiophys. Quantum Electron. 16, 783–789 (1973); applies only for a Kerr medium and no waveguide structures.

[CrossRef]

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538–1541 (1997).

[CrossRef]

M. I. Weinstein, “Lyapunov stability of ground state of nonlinear evolution equations,” SIAM J. Math. Anal. 16, 472–483 (1985).

[CrossRef]

A. L. Berkhoer and V. E. Zakharov, “Self-excitation of waves with different polarizations in nonlinear media,” Sov. Phys. JETP 31, 486–493 (1970) [Zh. Eksp. Teor. Fiz. 58, 903–911 (1970)].

S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Sov. Phys. JETP 38, 248–253 (1974) [Zh. Eksp. Teor. Fiz. 65, 505–516 (1973)].

S. A. Akhmanov, A. P. Sukhorukov, and R. V. Khokhlov, “Self-focusing and self-trapping of intense light beams in a nonlinear medium,” Sov. Phys. JETP 23, 1025–1033 (1966) [Zh. Eksp. Teor. Fiz. 50, 1537–1549 (1966)].

The use of the nonlinearity-induced refractive-index change created by an intense beam for guiding particles (electrons and atoms) was suggested even earlier; see G. A. Askar’yan, “Effect of the gradient of a strong electromagnetic beam on electrons and atoms,” Sov. Phys. JETP 15, 1088–1090 (1962) [Zh. Eksp. Teor. Fiz. 42, 1567–1570 (1962)].

As spatially localized solutions of the defocusing cubic nonlinear Schrödinger equation, vortex solitons were first introduced by V. L. Ginzburg and L. P. Pitaevski, “On the theory of superfluidity,” Sov. Phys. JETP 7, 858–861 (1959) [Zh. Eksp. Teor. Fiz. 34, 1240–1245 (1958)]; see also L. P. Pitaevski, “Vortex lines in an imperfect Bose gas,” Sov. Phys. JETP 13, 451–454 (1961) [Zh. Eksp. Teor. Fiz. 40, 646–651 (1961)], on topological excitations in superfluids. The term vortex had been used much earlier for different (linear) physical processes and for different defining equations.

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Zh. Eksp. Teor. Fiz. 61, 118–134 (1971) [Sov. Phys. JETP 34, 62–69 (1972)].

Yu. N. Karamzin and A. P. Sukhorukov, “Mutual focusing of high-power light beams in media with quadratic nonlinearity,” Zh. Eksp. Teor. Fiz. 68, 834–847 (1975) [Sov. Phys. JETP 41, 414–420 (1976)]; A. V. Buryak and Yu. S. Kivshar, “Spatial optical solitons governed by quadratic nonlinearity,” Opt. Lett. 19, 1612–1614 (1994); L. Torner, C. R. Menyuk, and G. I. Stegeman, “Excitation of solitons with cascaded χ(2) nonlinearity,” Opt. Lett. 19, 1615–1617 (1994).

[CrossRef]
[PubMed]

Yu. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. (to be published).

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1985).

A. W. Snyder, D. J. Mitchell, and Yu. S. Kivshar, “Linear perspective of solitons,” in Physics and Applications of Optical Solitons in Fibers, A. Hasegawa, ed. (Kluwer Academic, Amsterdam, 1996), pp. 263–275.

V. Tikhonenko, Laser Physics Centre, Australian National University, ACT 0200 Canberra, Australia (personal communication, 1997).