S. Pitois, S. Lagrange, H. R. Jauslin, and A. Picozzi, “Velocity Locking of Incoherent Nonlinear Wave Packets,” Phys. Rev. Lett. 97, 033902-5 (2006).

[CrossRef]
[PubMed]

H. Buljan, M. Segev, and A. Vardi, “Incoherent Matter-Wave Solitons and Pairing Instability in an Attractively Interacting Bose-Einstein Condensate,” Phys. Rev. Lett. 95, 180401-4 (2005).

[CrossRef]
[PubMed]

T. Schwartz, T. Carmon, H. Buljan, and M. Segev, “Spontaneous Pattern Formation with Incoherent White Light,” Phys. Rev. Lett. 93, 223901-5 (2004).

[CrossRef]
[PubMed]

D. Anderson, L. Helczynski-Wolf, M. Lisak, and V. Semenov,“Features of modulational instability of partially coherent light: Importance of the incoherence spectrum,” Phys. Rev. E 69, 025601–025604 (2004).

[CrossRef]

M. Soljačić, K. Steiglitz, S. M. Sears, M. Segev, M. H. Jakubowski, and R. Squie, “Collisions of Two Solitons in an Arbitrary Number of Coupled Nonlinear Schrödinger Equations,” Phys. Rev. Lett. 90, 254102–254105 (2003).

[CrossRef]
[PubMed]

D. Anderson, B. Hall, M. Lisak, and M. Marklund, “Statistical effects in the multistream model for quantum plasmas,” Phys. Rev. E 65, 046417-5 (2002).

[CrossRef]

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, “Clustering of solitons in weakly correlated wavefronts,” PNAS 99, 5223–5227 (2002).

[CrossRef]

S. M. Sears, M. Soljačić, D. N. Christodoulides, and M. Segev, “Pattern formation via symmetry breaking in nonlinear weakly correlated systems,” Phys. Rev. E 65, 036620–9 (2002).

[CrossRef]

H. Buljan, A. Šiber, M. Soljačić, and M. Segev, “Propagation of incoherent “white” light and modulation instability in noninstantaneous nonlinear media,” Phys. Rev. E 66, 035601-4 (2002).

[CrossRef]

D. Kip, M. Soljacic, M. Segev, S. M. Sears, and D. N. Christodoulides, “(1+1)-Dimensional modulation instability of spatially incoherent light,” J. Opt. Soc. Am. B 19, 502–512 (2002).

[CrossRef]

J. Klinger, H. Martin, and Z. Chen, “Experiments on induced modulational instability of an incoherent optical beam,” Opt. Lett. 26, 271–273 (2001).

[CrossRef]

R. Malendevich, L. Jankovic, G. Stegeman, and J. Stewart Aitchison, “Spatial modulation instability in a Kerr slab waveguide,” Opt. Lett. 26, 1879–1881 (2001).

[CrossRef]

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, and M. Segev,“Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media,” Phys. Rev. E 63, 035601–035603 (R) (2001).

[CrossRef]

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation Instability of Incoherent Beams in Noninstantaneous Nonlinear Media,” Phys. Rev. Lett. 84, 467–470 (2000).

[CrossRef]
[PubMed]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation Instability and Pattern Formation in Spatially Incoherent Light Beams,” Science 290, 495–498 (2000).

[CrossRef]
[PubMed]

F. T. Arecchi, S. Boccaletti, and P. Ramazza, “Pattern formation and competition in nonlinear optics,” Phys. Rep. 318, 1–83 (1999).

[CrossRef]

M. Mitchell and M. Segev, “Self-trapping of incoherent white light,” Nature (London) 387, 880–883 (1997).

[CrossRef]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Theory of Self-Trapped Spatially Incoherent Light Beams,” Phys. Rev. Lett. 79, 4990–4993 (1997).

[CrossRef]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-Trapping of Partially Spatially Incoherent Light,” Phys. Rev. Lett. 77, 490–493 (1996).

[CrossRef]
[PubMed]

M. D. Iturbe-Castillo, M. Torres-Cisneros, J. J. Sanchez-Mondragon, S. Chavez-Cerda, S. I. Stepanov, V. A. Vysloukh, and G. E. Torres-Cisneros, “Experimental evidence of modulation instability in a photorefractive Bi12TiO20 crystal,” Opt. Lett. 20, 1853 (1995).

[CrossRef]
[PubMed]

E. A. Kuznetsov, A. V. Mikhailov, and I. A. Shimokhin, “Nonlinear interaction of solitons and radiation,” Physica D 87, 201–215 (1995).

[CrossRef]

M. C. Cross and P. C. Hohenberg, “Pattern formation outside of equilibrium,” Rev. Mod. Phys. 65, 851–1112 (1993).

[CrossRef]

S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharo., “Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear,” Physica D (Amsterdam) 57, 96–160 (1992).

[CrossRef]

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).

[CrossRef]
[PubMed]

V.G. Makhan’kov and O. K. Pashaev, “Nonlinear Schrödinger equation with noncompact isogroup,” Teor. Mat. Fiz. 53, 55 (1982).

E. T. Jaynes, “Information Theory and Statistical Mechanics,” Phys. Rev. 106, 620–630 (1957).

[CrossRef]

E. T. Jaynes, “Information Theory and Statistical Mechanics. II,” Phys. Rev. 108, 171–190 (1957).

[CrossRef]

D. Anderson, L. Helczynski-Wolf, M. Lisak, and V. Semenov,“Features of modulational instability of partially coherent light: Importance of the incoherence spectrum,” Phys. Rev. E 69, 025601–025604 (2004).

[CrossRef]

D. Anderson, B. Hall, M. Lisak, and M. Marklund, “Statistical effects in the multistream model for quantum plasmas,” Phys. Rev. E 65, 046417-5 (2002).

[CrossRef]

F. T. Arecchi, S. Boccaletti, and P. Ramazza, “Pattern formation and competition in nonlinear optics,” Phys. Rep. 318, 1–83 (1999).

[CrossRef]

V. I. Bespalov and V. I. Talanov, “Filamentary Structure of Light Beams in Nonlinear Liquids,” Zh. Eksperim. i Teor. Fiz.-Pis’ma Redakt.3, 471 (1966); [translation: JETP Letters 3, 307–312 (1966)].

F. T. Arecchi, S. Boccaletti, and P. Ramazza, “Pattern formation and competition in nonlinear optics,” Phys. Rep. 318, 1–83 (1999).

[CrossRef]

R. W. Boyd, Nonlinear Optics (Academic Press, New York, 1994).

H. Buljan, M. Segev, and A. Vardi, “Incoherent Matter-Wave Solitons and Pairing Instability in an Attractively Interacting Bose-Einstein Condensate,” Phys. Rev. Lett. 95, 180401-4 (2005).

[CrossRef]
[PubMed]

T. Schwartz, T. Carmon, H. Buljan, and M. Segev, “Spontaneous Pattern Formation with Incoherent White Light,” Phys. Rev. Lett. 93, 223901-5 (2004).

[CrossRef]
[PubMed]

H. Buljan, A. Šiber, M. Soljačić, and M. Segev, “Propagation of incoherent “white” light and modulation instability in noninstantaneous nonlinear media,” Phys. Rev. E 66, 035601-4 (2002).

[CrossRef]

T. Schwartz, T. Carmon, H. Buljan, and M. Segev, “Spontaneous Pattern Formation with Incoherent White Light,” Phys. Rev. Lett. 93, 223901-5 (2004).

[CrossRef]
[PubMed]

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, “Clustering of solitons in weakly correlated wavefronts,” PNAS 99, 5223–5227 (2002).

[CrossRef]

J. Klinger, H. Martin, and Z. Chen, “Experiments on induced modulational instability of an incoherent optical beam,” Opt. Lett. 26, 271–273 (2001).

[CrossRef]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-Trapping of Partially Spatially Incoherent Light,” Phys. Rev. Lett. 77, 490–493 (1996).

[CrossRef]
[PubMed]

D. Kip, M. Soljacic, M. Segev, S. M. Sears, and D. N. Christodoulides, “(1+1)-Dimensional modulation instability of spatially incoherent light,” J. Opt. Soc. Am. B 19, 502–512 (2002).

[CrossRef]

S. M. Sears, M. Soljačić, D. N. Christodoulides, and M. Segev, “Pattern formation via symmetry breaking in nonlinear weakly correlated systems,” Phys. Rev. E 65, 036620–9 (2002).

[CrossRef]

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, “Clustering of solitons in weakly correlated wavefronts,” PNAS 99, 5223–5227 (2002).

[CrossRef]

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, and M. Segev,“Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media,” Phys. Rev. E 63, 035601–035603 (R) (2001).

[CrossRef]

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation Instability of Incoherent Beams in Noninstantaneous Nonlinear Media,” Phys. Rev. Lett. 84, 467–470 (2000).

[CrossRef]
[PubMed]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation Instability and Pattern Formation in Spatially Incoherent Light Beams,” Science 290, 495–498 (2000).

[CrossRef]
[PubMed]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Theory of Self-Trapped Spatially Incoherent Light Beams,” Phys. Rev. Lett. 79, 4990–4993 (1997).

[CrossRef]

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation Instability of Incoherent Beams in Noninstantaneous Nonlinear Media,” Phys. Rev. Lett. 84, 467–470 (2000).

[CrossRef]
[PubMed]

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, and M. Segev,“Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media,” Phys. Rev. E 63, 035601–035603 (R) (2001).

[CrossRef]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Theory of Self-Trapped Spatially Incoherent Light Beams,” Phys. Rev. Lett. 79, 4990–4993 (1997).

[CrossRef]

M. C. Cross and P. C. Hohenberg, “Pattern formation outside of equilibrium,” Rev. Mod. Phys. 65, 851–1112 (1993).

[CrossRef]

S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharo., “Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear,” Physica D (Amsterdam) 57, 96–160 (1992).

[CrossRef]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation Instability and Pattern Formation in Spatially Incoherent Light Beams,” Science 290, 495–498 (2000).

[CrossRef]
[PubMed]

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, and M. Segev,“Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media,” Phys. Rev. E 63, 035601–035603 (R) (2001).

[CrossRef]

E. Fermi, J. Pasta, and S. Ulam, “Studies of non linear problems,” Los Alamos Rpt. LA-1940 (1955).

D. Anderson, B. Hall, M. Lisak, and M. Marklund, “Statistical effects in the multistream model for quantum plasmas,” Phys. Rev. E 65, 046417-5 (2002).

[CrossRef]

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).

[CrossRef]
[PubMed]

D. Anderson, L. Helczynski-Wolf, M. Lisak, and V. Semenov,“Features of modulational instability of partially coherent light: Importance of the incoherence spectrum,” Phys. Rev. E 69, 025601–025604 (2004).

[CrossRef]

M. C. Cross and P. C. Hohenberg, “Pattern formation outside of equilibrium,” Rev. Mod. Phys. 65, 851–1112 (1993).

[CrossRef]

M. Soljačić, K. Steiglitz, S. M. Sears, M. Segev, M. H. Jakubowski, and R. Squie, “Collisions of Two Solitons in an Arbitrary Number of Coupled Nonlinear Schrödinger Equations,” Phys. Rev. Lett. 90, 254102–254105 (2003).

[CrossRef]
[PubMed]

S. Pitois, S. Lagrange, H. R. Jauslin, and A. Picozzi, “Velocity Locking of Incoherent Nonlinear Wave Packets,” Phys. Rev. Lett. 97, 033902-5 (2006).

[CrossRef]
[PubMed]

E. T. Jaynes, “Information Theory and Statistical Mechanics,” Phys. Rev. 106, 620–630 (1957).

[CrossRef]

E. T. Jaynes, “Information Theory and Statistical Mechanics. II,” Phys. Rev. 108, 171–190 (1957).

[CrossRef]

D. Kip, M. Soljacic, M. Segev, S. M. Sears, and D. N. Christodoulides, “(1+1)-Dimensional modulation instability of spatially incoherent light,” J. Opt. Soc. Am. B 19, 502–512 (2002).

[CrossRef]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation Instability and Pattern Formation in Spatially Incoherent Light Beams,” Science 290, 495–498 (2000).

[CrossRef]
[PubMed]

E. A. Kuznetsov, A. V. Mikhailov, and I. A. Shimokhin, “Nonlinear interaction of solitons and radiation,” Physica D 87, 201–215 (1995).

[CrossRef]

S. Pitois, S. Lagrange, H. R. Jauslin, and A. Picozzi, “Velocity Locking of Incoherent Nonlinear Wave Packets,” Phys. Rev. Lett. 97, 033902-5 (2006).

[CrossRef]
[PubMed]

D. Anderson, L. Helczynski-Wolf, M. Lisak, and V. Semenov,“Features of modulational instability of partially coherent light: Importance of the incoherence spectrum,” Phys. Rev. E 69, 025601–025604 (2004).

[CrossRef]

D. Anderson, B. Hall, M. Lisak, and M. Marklund, “Statistical effects in the multistream model for quantum plasmas,” Phys. Rev. E 65, 046417-5 (2002).

[CrossRef]

L. A. Lugiato, Chaos Solitons Fractals 4, 1245–1251 (1994).

V.G. Makhan’kov and O. K. Pashaev, “Nonlinear Schrödinger equation with noncompact isogroup,” Teor. Mat. Fiz. 53, 55 (1982).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge University Press, 1995).

D. Anderson, B. Hall, M. Lisak, and M. Marklund, “Statistical effects in the multistream model for quantum plasmas,” Phys. Rev. E 65, 046417-5 (2002).

[CrossRef]

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, “Clustering of solitons in weakly correlated wavefronts,” PNAS 99, 5223–5227 (2002).

[CrossRef]

J. Klinger, H. Martin, and Z. Chen, “Experiments on induced modulational instability of an incoherent optical beam,” Opt. Lett. 26, 271–273 (2001).

[CrossRef]

E. A. Kuznetsov, A. V. Mikhailov, and I. A. Shimokhin, “Nonlinear interaction of solitons and radiation,” Physica D 87, 201–215 (1995).

[CrossRef]

M. Mitchell and M. Segev, “Self-trapping of incoherent white light,” Nature (London) 387, 880–883 (1997).

[CrossRef]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Theory of Self-Trapped Spatially Incoherent Light Beams,” Phys. Rev. Lett. 79, 4990–4993 (1997).

[CrossRef]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-Trapping of Partially Spatially Incoherent Light,” Phys. Rev. Lett. 77, 490–493 (1996).

[CrossRef]
[PubMed]

S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharo., “Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear,” Physica D (Amsterdam) 57, 96–160 (1992).

[CrossRef]

V.G. Makhan’kov and O. K. Pashaev, “Nonlinear Schrödinger equation with noncompact isogroup,” Teor. Mat. Fiz. 53, 55 (1982).

E. Fermi, J. Pasta, and S. Ulam, “Studies of non linear problems,” Los Alamos Rpt. LA-1940 (1955).

S. Pitois, S. Lagrange, H. R. Jauslin, and A. Picozzi, “Velocity Locking of Incoherent Nonlinear Wave Packets,” Phys. Rev. Lett. 97, 033902-5 (2006).

[CrossRef]
[PubMed]

S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharo., “Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear,” Physica D (Amsterdam) 57, 96–160 (1992).

[CrossRef]

F. T. Arecchi, S. Boccaletti, and P. Ramazza, “Pattern formation and competition in nonlinear optics,” Phys. Rep. 318, 1–83 (1999).

[CrossRef]

The only exception we know of is M. Rigolet al., Phys. Rev. Lett.98, 050405-5 (2007) where a quantum integrable system relaxes to a steady state, carrying memory of initial conditions.

[CrossRef]
[PubMed]

T. Schwartz, T. Carmon, H. Buljan, and M. Segev, “Spontaneous Pattern Formation with Incoherent White Light,” Phys. Rev. Lett. 93, 223901-5 (2004).

[CrossRef]
[PubMed]

M. Soljačić, K. Steiglitz, S. M. Sears, M. Segev, M. H. Jakubowski, and R. Squie, “Collisions of Two Solitons in an Arbitrary Number of Coupled Nonlinear Schrödinger Equations,” Phys. Rev. Lett. 90, 254102–254105 (2003).

[CrossRef]
[PubMed]

D. Kip, M. Soljacic, M. Segev, S. M. Sears, and D. N. Christodoulides, “(1+1)-Dimensional modulation instability of spatially incoherent light,” J. Opt. Soc. Am. B 19, 502–512 (2002).

[CrossRef]

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, “Clustering of solitons in weakly correlated wavefronts,” PNAS 99, 5223–5227 (2002).

[CrossRef]

S. M. Sears, M. Soljačić, D. N. Christodoulides, and M. Segev, “Pattern formation via symmetry breaking in nonlinear weakly correlated systems,” Phys. Rev. E 65, 036620–9 (2002).

[CrossRef]

H. Buljan, M. Segev, and A. Vardi, “Incoherent Matter-Wave Solitons and Pairing Instability in an Attractively Interacting Bose-Einstein Condensate,” Phys. Rev. Lett. 95, 180401-4 (2005).

[CrossRef]
[PubMed]

T. Schwartz, T. Carmon, H. Buljan, and M. Segev, “Spontaneous Pattern Formation with Incoherent White Light,” Phys. Rev. Lett. 93, 223901-5 (2004).

[CrossRef]
[PubMed]

M. Soljačić, K. Steiglitz, S. M. Sears, M. Segev, M. H. Jakubowski, and R. Squie, “Collisions of Two Solitons in an Arbitrary Number of Coupled Nonlinear Schrödinger Equations,” Phys. Rev. Lett. 90, 254102–254105 (2003).

[CrossRef]
[PubMed]

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, “Clustering of solitons in weakly correlated wavefronts,” PNAS 99, 5223–5227 (2002).

[CrossRef]

D. Kip, M. Soljacic, M. Segev, S. M. Sears, and D. N. Christodoulides, “(1+1)-Dimensional modulation instability of spatially incoherent light,” J. Opt. Soc. Am. B 19, 502–512 (2002).

[CrossRef]

S. M. Sears, M. Soljačić, D. N. Christodoulides, and M. Segev, “Pattern formation via symmetry breaking in nonlinear weakly correlated systems,” Phys. Rev. E 65, 036620–9 (2002).

[CrossRef]

H. Buljan, A. Šiber, M. Soljačić, and M. Segev, “Propagation of incoherent “white” light and modulation instability in noninstantaneous nonlinear media,” Phys. Rev. E 66, 035601-4 (2002).

[CrossRef]

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, and M. Segev,“Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media,” Phys. Rev. E 63, 035601–035603 (R) (2001).

[CrossRef]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation Instability and Pattern Formation in Spatially Incoherent Light Beams,” Science 290, 495–498 (2000).

[CrossRef]
[PubMed]

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation Instability of Incoherent Beams in Noninstantaneous Nonlinear Media,” Phys. Rev. Lett. 84, 467–470 (2000).

[CrossRef]
[PubMed]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Theory of Self-Trapped Spatially Incoherent Light Beams,” Phys. Rev. Lett. 79, 4990–4993 (1997).

[CrossRef]

M. Mitchell and M. Segev, “Self-trapping of incoherent white light,” Nature (London) 387, 880–883 (1997).

[CrossRef]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-Trapping of Partially Spatially Incoherent Light,” Phys. Rev. Lett. 77, 490–493 (1996).

[CrossRef]
[PubMed]

D. Anderson, L. Helczynski-Wolf, M. Lisak, and V. Semenov,“Features of modulational instability of partially coherent light: Importance of the incoherence spectrum,” Phys. Rev. E 69, 025601–025604 (2004).

[CrossRef]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-Trapping of Partially Spatially Incoherent Light,” Phys. Rev. Lett. 77, 490–493 (1996).

[CrossRef]
[PubMed]

E. A. Kuznetsov, A. V. Mikhailov, and I. A. Shimokhin, “Nonlinear interaction of solitons and radiation,” Physica D 87, 201–215 (1995).

[CrossRef]

H. Buljan, A. Šiber, M. Soljačić, and M. Segev, “Propagation of incoherent “white” light and modulation instability in noninstantaneous nonlinear media,” Phys. Rev. E 66, 035601-4 (2002).

[CrossRef]

M. Soljačić, K. Steiglitz, S. M. Sears, M. Segev, M. H. Jakubowski, and R. Squie, “Collisions of Two Solitons in an Arbitrary Number of Coupled Nonlinear Schrödinger Equations,” Phys. Rev. Lett. 90, 254102–254105 (2003).

[CrossRef]
[PubMed]

H. Buljan, A. Šiber, M. Soljačić, and M. Segev, “Propagation of incoherent “white” light and modulation instability in noninstantaneous nonlinear media,” Phys. Rev. E 66, 035601-4 (2002).

[CrossRef]

D. Kip, M. Soljacic, M. Segev, S. M. Sears, and D. N. Christodoulides, “(1+1)-Dimensional modulation instability of spatially incoherent light,” J. Opt. Soc. Am. B 19, 502–512 (2002).

[CrossRef]

S. M. Sears, M. Soljačić, D. N. Christodoulides, and M. Segev, “Pattern formation via symmetry breaking in nonlinear weakly correlated systems,” Phys. Rev. E 65, 036620–9 (2002).

[CrossRef]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation Instability and Pattern Formation in Spatially Incoherent Light Beams,” Science 290, 495–498 (2000).

[CrossRef]
[PubMed]

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation Instability of Incoherent Beams in Noninstantaneous Nonlinear Media,” Phys. Rev. Lett. 84, 467–470 (2000).

[CrossRef]
[PubMed]

M. Soljačić, K. Steiglitz, S. M. Sears, M. Segev, M. H. Jakubowski, and R. Squie, “Collisions of Two Solitons in an Arbitrary Number of Coupled Nonlinear Schrödinger Equations,” Phys. Rev. Lett. 90, 254102–254105 (2003).

[CrossRef]
[PubMed]

M. Soljačić, K. Steiglitz, S. M. Sears, M. Segev, M. H. Jakubowski, and R. Squie, “Collisions of Two Solitons in an Arbitrary Number of Coupled Nonlinear Schrödinger Equations,” Phys. Rev. Lett. 90, 254102–254105 (2003).

[CrossRef]
[PubMed]

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).

[CrossRef]
[PubMed]

V. I. Bespalov and V. I. Talanov, “Filamentary Structure of Light Beams in Nonlinear Liquids,” Zh. Eksperim. i Teor. Fiz.-Pis’ma Redakt.3, 471 (1966); [translation: JETP Letters 3, 307–312 (1966)].

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).

[CrossRef]
[PubMed]

E. Fermi, J. Pasta, and S. Ulam, “Studies of non linear problems,” Los Alamos Rpt. LA-1940 (1955).

H. Buljan, M. Segev, and A. Vardi, “Incoherent Matter-Wave Solitons and Pairing Instability in an Attractively Interacting Bose-Einstein Condensate,” Phys. Rev. Lett. 95, 180401-4 (2005).

[CrossRef]
[PubMed]

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation Instability of Incoherent Beams in Noninstantaneous Nonlinear Media,” Phys. Rev. Lett. 84, 467–470 (2000).

[CrossRef]
[PubMed]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge University Press, 1995).

S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharo., “Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear,” Physica D (Amsterdam) 57, 96–160 (1992).

[CrossRef]

M. Mitchell and M. Segev, “Self-trapping of incoherent white light,” Nature (London) 387, 880–883 (1997).

[CrossRef]

J. Klinger, H. Martin, and Z. Chen, “Experiments on induced modulational instability of an incoherent optical beam,” Opt. Lett. 26, 271–273 (2001).

[CrossRef]

M. D. Iturbe-Castillo, M. Torres-Cisneros, J. J. Sanchez-Mondragon, S. Chavez-Cerda, S. I. Stepanov, V. A. Vysloukh, and G. E. Torres-Cisneros, “Experimental evidence of modulation instability in a photorefractive Bi12TiO20 crystal,” Opt. Lett. 20, 1853 (1995).

[CrossRef]
[PubMed]

R. Malendevich, L. Jankovic, G. Stegeman, and J. Stewart Aitchison, “Spatial modulation instability in a Kerr slab waveguide,” Opt. Lett. 26, 1879–1881 (2001).

[CrossRef]

F. T. Arecchi, S. Boccaletti, and P. Ramazza, “Pattern formation and competition in nonlinear optics,” Phys. Rep. 318, 1–83 (1999).

[CrossRef]

E. T. Jaynes, “Information Theory and Statistical Mechanics,” Phys. Rev. 106, 620–630 (1957).

[CrossRef]

E. T. Jaynes, “Information Theory and Statistical Mechanics. II,” Phys. Rev. 108, 171–190 (1957).

[CrossRef]

D. Anderson, L. Helczynski-Wolf, M. Lisak, and V. Semenov,“Features of modulational instability of partially coherent light: Importance of the incoherence spectrum,” Phys. Rev. E 69, 025601–025604 (2004).

[CrossRef]

D. Anderson, B. Hall, M. Lisak, and M. Marklund, “Statistical effects in the multistream model for quantum plasmas,” Phys. Rev. E 65, 046417-5 (2002).

[CrossRef]

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, and M. Segev,“Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media,” Phys. Rev. E 63, 035601–035603 (R) (2001).

[CrossRef]

S. M. Sears, M. Soljačić, D. N. Christodoulides, and M. Segev, “Pattern formation via symmetry breaking in nonlinear weakly correlated systems,” Phys. Rev. E 65, 036620–9 (2002).

[CrossRef]

H. Buljan, A. Šiber, M. Soljačić, and M. Segev, “Propagation of incoherent “white” light and modulation instability in noninstantaneous nonlinear media,” Phys. Rev. E 66, 035601-4 (2002).

[CrossRef]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Theory of Self-Trapped Spatially Incoherent Light Beams,” Phys. Rev. Lett. 79, 4990–4993 (1997).

[CrossRef]

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation Instability of Incoherent Beams in Noninstantaneous Nonlinear Media,” Phys. Rev. Lett. 84, 467–470 (2000).

[CrossRef]
[PubMed]

T. Schwartz, T. Carmon, H. Buljan, and M. Segev, “Spontaneous Pattern Formation with Incoherent White Light,” Phys. Rev. Lett. 93, 223901-5 (2004).

[CrossRef]
[PubMed]

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).

[CrossRef]
[PubMed]

S. Pitois, S. Lagrange, H. R. Jauslin, and A. Picozzi, “Velocity Locking of Incoherent Nonlinear Wave Packets,” Phys. Rev. Lett. 97, 033902-5 (2006).

[CrossRef]
[PubMed]

M. Soljačić, K. Steiglitz, S. M. Sears, M. Segev, M. H. Jakubowski, and R. Squie, “Collisions of Two Solitons in an Arbitrary Number of Coupled Nonlinear Schrödinger Equations,” Phys. Rev. Lett. 90, 254102–254105 (2003).

[CrossRef]
[PubMed]

H. Buljan, M. Segev, and A. Vardi, “Incoherent Matter-Wave Solitons and Pairing Instability in an Attractively Interacting Bose-Einstein Condensate,” Phys. Rev. Lett. 95, 180401-4 (2005).

[CrossRef]
[PubMed]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-Trapping of Partially Spatially Incoherent Light,” Phys. Rev. Lett. 77, 490–493 (1996).

[CrossRef]
[PubMed]

S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharo., “Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear,” Physica D (Amsterdam) 57, 96–160 (1992).

[CrossRef]

E. A. Kuznetsov, A. V. Mikhailov, and I. A. Shimokhin, “Nonlinear interaction of solitons and radiation,” Physica D 87, 201–215 (1995).

[CrossRef]

Z. Chen, S. M. Sears, H. Martin, D. N. Christodoulides, and M. Segev, “Clustering of solitons in weakly correlated wavefronts,” PNAS 99, 5223–5227 (2002).

[CrossRef]

M. C. Cross and P. C. Hohenberg, “Pattern formation outside of equilibrium,” Rev. Mod. Phys. 65, 851–1112 (1993).

[CrossRef]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation Instability and Pattern Formation in Spatially Incoherent Light Beams,” Science 290, 495–498 (2000).

[CrossRef]
[PubMed]

V.G. Makhan’kov and O. K. Pashaev, “Nonlinear Schrödinger equation with noncompact isogroup,” Teor. Mat. Fiz. 53, 55 (1982).

The only exception we know of is M. Rigolet al., Phys. Rev. Lett.98, 050405-5 (2007) where a quantum integrable system relaxes to a steady state, carrying memory of initial conditions.

[CrossRef]
[PubMed]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge University Press, 1995).

E. Fermi, J. Pasta, and S. Ulam, “Studies of non linear problems,” Los Alamos Rpt. LA-1940 (1955).

V. I. Bespalov and V. I. Talanov, “Filamentary Structure of Light Beams in Nonlinear Liquids,” Zh. Eksperim. i Teor. Fiz.-Pis’ma Redakt.3, 471 (1966); [translation: JETP Letters 3, 307–312 (1966)].

R. W. Boyd, Nonlinear Optics (Academic Press, New York, 1994).

L. A. Lugiato, Chaos Solitons Fractals 4, 1245–1251 (1994).