J. T. Mok, C. M. de Sterke, I. C. M. Litte, and B. J. Eggleton, “Dispersionless slow light using gap solitons,” Nat. Phys. 2, 775-780 (2006).

[CrossRef]

D. R. Neill and J. Atai, “Collision dynamics of gap solitons in Kerr media,” Phys. Lett. A 353, 416-421 (2006).

[CrossRef]

K. Yagasaki, I. M. Merhasin, B. A. Malomed, T. Wagenknecht, and A. R. Champneys, “Gap solitons in Bragg gratings with a harmonic superlattice,” Europhys. Lett. 74, 1006-1012 (2006).

[CrossRef]

N. C. Panoiu, R. M. Osgood, and B. A. Malomed, “Semi-discrete composite solitons in arrays of quadratically nonlinear waveguides,” Opt. Lett. 31, 1097-1099 (2006).

[CrossRef]
[PubMed]

O. F. Oxtoby, D. E. Pelinovsky, and I. V. Barashenkov, “Travelling kinks in discrete phi(4) models,” Nonlinearity 19, 217-235 (2006).

[CrossRef]

B. A. Malomed, J. Fujioka, A. Espinosa-Ceron, R. F. Rodriguez, and S. González, “Moving embedded lattice solitons,” Chaos 16, 013112 (2006).

[CrossRef]
[PubMed]

D. E. Pelinovsky and V. M. Rothos, “Bifurcations of travelling wave solutions in the discrete NLS equations,” Physica D 202, 16-36 (2005).

[CrossRef]

I. M. Merhasin, B. V. Gisin, R. Driben, and B. A. Malomed, “Finite-band solitons in the Kronig-Penney model with the cubic-quintic nonlinearity,” Phys. Rev. E 71, 016613 (2005).

[CrossRef]

P. Y. P. Chen, B. A. Malomed, and P. L. Chu, “Trapping Bragg solitons by a pair of defects,” Phys. Rev. E 71, 066601 (2005).

[CrossRef]

F. Chen, M. Stepic, C. E. Rüter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, “Discrete diffraction and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays,” Opt. Express 13, 4314-4324 (2005).

[CrossRef]
[PubMed]

G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, “Spatial photonics in nonlinear waveguide arrays,” Opt. Express 13, 1780-1796 (2005).

[CrossRef]
[PubMed]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Yu. S. Kivshar, “Controlled generation and steering of spatial gap solitons,” Phys. Rev. Lett. 93, 083905 (2004).

[CrossRef]
[PubMed]

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904 (2004).

[CrossRef]
[PubMed]

R. Morandotti, D. Mandelik, Y. Silberberg, J. S. Aitchison, M. Sorel, D. N. Christodoulides, A. A. Sukhorukov, and Y. S. Kivshar, “Observation of discrete gap solitons in binary waveguide arrays,” Opt. Lett. 29, 2890-2892 (2004).

[CrossRef]

W. Li and A. Smerzi, Phys. Rev. E 70, 016605 (2004).

[CrossRef]

W. C. K. Mak, B. A. Malomed, and P. L. Chu, “Slowdown and splitting of gap solitons in apodized Bragg Gratings,” J. Mod. Opt. 51, 2141-2158 (2004).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Dynamics of positive- and negative-mass solitons in optical lattices and inverted traps,” J. Phys. B 37, 1443-1459 (2004).

[CrossRef]

B. Eiermann, Th. Anker, M. Albiez, M. Taglieber, P. Treutlein, K.-P. Marzlin, and M. K. Oberthaler, “Bright Bose-Einstein gap solitons of atoms with repulsive interaction,” Phys. Rev. Lett. 92, 230401 (2004).

[CrossRef]
[PubMed]

E. A. Ostrovskaya and Yu. S. Kivshar, “Matter-wave gap solitons in atomic band-gap structures,” Phys. Rev. Lett. 90, 160407 (2003).

[CrossRef]
[PubMed]

P. G. Kevrekidis, “On a class of discretizations of Hamiltonian nonlinear partial differential equations,” Physica D 183, 68-86 (2003).

[CrossRef]

I. E. Papacharalampous, P. G. Kevrekidis, B. A. Malomed, and D. J. Frantzeskakis, “Soliton collisions in the discrete nonlinear Schrödinger equation,” Phys. Rev. E 68, 046604 (2003).

[CrossRef]

W. C. K. Mak, B. A. Malomed, and P. L. Chu, “Formation of a standing-light pulse through collision of gap solitons,” Phys. Rev. E 68, 026609 (2003).

[CrossRef]

W. C. K. Mak, B. A. Malomed, and P. L. Chu, “Interaction of a soliton with a localized gain in a fiber Bragg grating,” Phys. Rev. E 67, 026608 (2003).

[CrossRef]

W. C. K. Mak, B. A. Malomed, and P. L. Chu, “Interaction of a soliton with a local defect in a fiber Bragg grating,” J. Opt. Soc. Am. B 20, 725-735 (2003).

[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).

[CrossRef]
[PubMed]

W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147-150 (2003).

[CrossRef]
[PubMed]

P. G. Kevrekidis, B. A. Malomed, and Z. Musslimani, “Discrete gap solitons in a diffraction-managed waveguide array,” Eur. Phys. J. D 23, 421-236 (2003).

[CrossRef]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. 90, 053902 (2003).

[CrossRef]
[PubMed]

A. A. Sukhorukov and Yu. S. Kivshar, “Discrete gap solitons in modulated waveguide arrays,” Opt. Lett. 27, 2112-2114 (2002).

[CrossRef]

R. H. Goodman, R. E. Slusher, and M. I. Weinstein, “Stopping light on a defect,” J. Opt. Soc. Am. B 19, 1635-1652 (2002).

[CrossRef]

J. Atai and B. A. Malomed, “Spatial solitons in a medium composed of self-focusing and self-defocusing layers,” Phys. Lett. A 298, 140-148 (2002).

[CrossRef]

M. J. Ablowitz, Z. H. Musslimani, and G. Biondini, “Methods for discrete solitons in nonlinear lattices,” Phys. Rev. E 65, 026602 (2002).

[CrossRef]

I. Carrusotto, D. Embriaco, and G. C. La Rocca, “Nonlinear atom optics and bright-gap-soliton generation in finite optical lattices,” Phys. Rev. A 65, 053611 (2002).

[CrossRef]

B. B. Baizakov, V. V. Konotop, and M. Salerno, “Regular spatial structures in arrays of Bose-Einstein condensates induced by modulational instability,” J. Phys. B 35, 5105-5119 (2002).

[CrossRef]

R. Driben and B. A. Malomed, “Suppression of crosstalk between solitons in a multi-channel split-step system,” Opt. Commun. 197, 481-489 (2001).

[CrossRef]

R. Driben and B. A. Malomed, “Split-step solitons in long fiber links,” Opt. Commun. 185, 439-456 (2000).

[CrossRef]

B. J. Eggleton, A. Ahuja, P. S. Westbrook, J. A. Rogers, P. Kuo, T. N. Nielsen, and B. Mikkelsen, “Integrated tunable fiber gratings for dispersion management in high-bit rate systems,” J. Lightwave Technol. 18, 1418-1432 (2000).

[CrossRef]

B. J. Eggleton, C. M. De Sterke, and R. E. Slusher, “Bragg solitons in the nonlinear Schrödinger limit: experiment and theory,” J. Opt. Soc. Am. B 16, 587-599 (1999).

[CrossRef]

L. Torner, “Walkoff-compensated dispersion-mapped quadratic solitons,” IEEE Photon. Technol. Lett. 11, 1268-1270 (1999).

[CrossRef]

S. Flach, Y. Zolotaryuk, and K. Kladko, “Moving lattice kinks and pulses: An inverse method,” Phys. Rev. E 59, 6105-6115 (1999).

[CrossRef]

N. M. Litchinitser, B. J. Eggleton, C. M. de Sterke, A. B. Aceves, and G. P. Agrawal, “Interaction of Bragg solitons in fiber gratings,” J. Opt. Soc. Am. B 16, 18-23 (1999).

[CrossRef]

I. V. Barashenkov, D. E. Pelinovsky, and E. V. Zemlyanaya, “Vibrations and oscillatory instabilities of gap solitons,” Phys. Rev. Lett. 80, 5117-5120 (1998).

[CrossRef]

A. De Rossi, C. Conti, and S. Trillo, “Stability, multistability, and wobbling of optical gap solitons,” Phys. Rev. Lett. 81, 85-88 (1998).

[CrossRef]

A. Othonos, “Fiber Bragg gratings,” Rev. Sci. Instrum. 68, 4309-4341 (1997).

[CrossRef]

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627-1630 (1996).

[CrossRef]
[PubMed]

F. Ouelette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broad-band and WDM dispersion compensationusing chirped sampled fiber Bragg gratings,” Electron. Lett. 31, 899-901 (1995).

[CrossRef]

B. A. Malomed and R. S. Tasgal, “Vibration modes of a gap soliton in a nonlinear optical medium,” Phys. Rev. E 49, 5787-5796 (1994).

[CrossRef]

D. B. Duncan, J. C. Eilbeck, H. Feddersen, and J. A. D. Wattis, “Solitons on lattices,” Physica D 68, 1-11 (1993).

[CrossRef]

D. N. Christodoulides and R. I. Joseph, “Slow Bragg solitons in nonlinear periodic structure,” Phys. Rev. Lett. 62, 1746-1749 (1989).

[CrossRef]
[PubMed]

A. B. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic media,” Phys. Lett. A 141, 37-42 (1989).

[CrossRef]

W. Chen and D. L. Mills, “Gap solitons and the nonlinear-optical response of superlattices,” Phys. Rev. Lett. 58, 160-163 (1987).

[CrossRef]
[PubMed]

P. St. J. Russell, “Optical superlattices for modulation and deflection of light,” J. Appl. Phys. 59, 3344-3355 (1986).

[CrossRef]

Yu. I. Voloshchenko, Yu. N. Ryzhov, and V. E. Sotin, “Stationary waves in nonlinear, periodically modulated media with large group retardation,” Zh. Tekh. Fiz. 51, 902 (1981) Yu. I. Voloshchenko, Yu. N. Ryzhov, and V. E. Sotin,[Sov. Phys. Tech. Phys. 26, 541 (1981)].

H. G. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379-381 (1979).

[CrossRef]

N. G. R. Broderick and C. M. de Sterke, “Theory of grating superstructures,” Phys. Rev. E 55, 3634-3646 (1977).

[CrossRef]

H. G. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379-381 (1979).

[CrossRef]

B. A. Malomed, J. Fujioka, A. Espinosa-Ceron, R. F. Rodriguez, and S. González, “Moving embedded lattice solitons,” Chaos 16, 013112 (2006).

[CrossRef]
[PubMed]

F. Ouelette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broad-band and WDM dispersion compensationusing chirped sampled fiber Bragg gratings,” Electron. Lett. 31, 899-901 (1995).

[CrossRef]

P. G. Kevrekidis, B. A. Malomed, and Z. Musslimani, “Discrete gap solitons in a diffraction-managed waveguide array,” Eur. Phys. J. D 23, 421-236 (2003).

[CrossRef]

K. Yagasaki, I. M. Merhasin, B. A. Malomed, T. Wagenknecht, and A. R. Champneys, “Gap solitons in Bragg gratings with a harmonic superlattice,” Europhys. Lett. 74, 1006-1012 (2006).

[CrossRef]

L. Torner, “Walkoff-compensated dispersion-mapped quadratic solitons,” IEEE Photon. Technol. Lett. 11, 1268-1270 (1999).

[CrossRef]

P. St. J. Russell, “Optical superlattices for modulation and deflection of light,” J. Appl. Phys. 59, 3344-3355 (1986).

[CrossRef]

W. C. K. Mak, B. A. Malomed, and P. L. Chu, “Slowdown and splitting of gap solitons in apodized Bragg Gratings,” J. Mod. Opt. 51, 2141-2158 (2004).

[CrossRef]

N. M. Litchinitser, B. J. Eggleton, C. M. de Sterke, A. B. Aceves, and G. P. Agrawal, “Interaction of Bragg solitons in fiber gratings,” J. Opt. Soc. Am. B 16, 18-23 (1999).

[CrossRef]

B. J. Eggleton, C. M. De Sterke, and R. E. Slusher, “Bragg solitons in the nonlinear Schrödinger limit: experiment and theory,” J. Opt. Soc. Am. B 16, 587-599 (1999).

[CrossRef]

R. H. Goodman, R. E. Slusher, and M. I. Weinstein, “Stopping light on a defect,” J. Opt. Soc. Am. B 19, 1635-1652 (2002).

[CrossRef]

W. C. K. Mak, B. A. Malomed, and P. L. Chu, “Interaction of a soliton with a local defect in a fiber Bragg grating,” J. Opt. Soc. Am. B 20, 725-735 (2003).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Dynamics of positive- and negative-mass solitons in optical lattices and inverted traps,” J. Phys. B 37, 1443-1459 (2004).

[CrossRef]

B. B. Baizakov, V. V. Konotop, and M. Salerno, “Regular spatial structures in arrays of Bose-Einstein condensates induced by modulational instability,” J. Phys. B 35, 5105-5119 (2002).

[CrossRef]

J. T. Mok, C. M. de Sterke, I. C. M. Litte, and B. J. Eggleton, “Dispersionless slow light using gap solitons,” Nat. Phys. 2, 775-780 (2006).

[CrossRef]

W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147-150 (2003).

[CrossRef]
[PubMed]

O. F. Oxtoby, D. E. Pelinovsky, and I. V. Barashenkov, “Travelling kinks in discrete phi(4) models,” Nonlinearity 19, 217-235 (2006).

[CrossRef]

R. Driben and B. A. Malomed, “Split-step solitons in long fiber links,” Opt. Commun. 185, 439-456 (2000).

[CrossRef]

R. Driben and B. A. Malomed, “Suppression of crosstalk between solitons in a multi-channel split-step system,” Opt. Commun. 197, 481-489 (2001).

[CrossRef]

G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, “Spatial photonics in nonlinear waveguide arrays,” Opt. Express 13, 1780-1796 (2005).

[CrossRef]
[PubMed]

F. Chen, M. Stepic, C. E. Rüter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, “Discrete diffraction and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays,” Opt. Express 13, 4314-4324 (2005).

[CrossRef]
[PubMed]

R. Morandotti, D. Mandelik, Y. Silberberg, J. S. Aitchison, M. Sorel, D. N. Christodoulides, A. A. Sukhorukov, and Y. S. Kivshar, “Observation of discrete gap solitons in binary waveguide arrays,” Opt. Lett. 29, 2890-2892 (2004).

[CrossRef]

A. A. Sukhorukov and Yu. S. Kivshar, “Discrete gap solitons in modulated waveguide arrays,” Opt. Lett. 27, 2112-2114 (2002).

[CrossRef]

N. C. Panoiu, R. M. Osgood, and B. A. Malomed, “Semi-discrete composite solitons in arrays of quadratically nonlinear waveguides,” Opt. Lett. 31, 1097-1099 (2006).

[CrossRef]
[PubMed]

D. R. Neill and J. Atai, “Collision dynamics of gap solitons in Kerr media,” Phys. Lett. A 353, 416-421 (2006).

[CrossRef]

J. Atai and B. A. Malomed, “Spatial solitons in a medium composed of self-focusing and self-defocusing layers,” Phys. Lett. A 298, 140-148 (2002).

[CrossRef]

A. B. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic media,” Phys. Lett. A 141, 37-42 (1989).

[CrossRef]

I. Carrusotto, D. Embriaco, and G. C. La Rocca, “Nonlinear atom optics and bright-gap-soliton generation in finite optical lattices,” Phys. Rev. A 65, 053611 (2002).

[CrossRef]

M. J. Ablowitz, Z. H. Musslimani, and G. Biondini, “Methods for discrete solitons in nonlinear lattices,” Phys. Rev. E 65, 026602 (2002).

[CrossRef]

I. E. Papacharalampous, P. G. Kevrekidis, B. A. Malomed, and D. J. Frantzeskakis, “Soliton collisions in the discrete nonlinear Schrödinger equation,” Phys. Rev. E 68, 046604 (2003).

[CrossRef]

S. Flach, Y. Zolotaryuk, and K. Kladko, “Moving lattice kinks and pulses: An inverse method,” Phys. Rev. E 59, 6105-6115 (1999).

[CrossRef]

B. A. Malomed and R. S. Tasgal, “Vibration modes of a gap soliton in a nonlinear optical medium,” Phys. Rev. E 49, 5787-5796 (1994).

[CrossRef]

N. G. R. Broderick and C. M. de Sterke, “Theory of grating superstructures,” Phys. Rev. E 55, 3634-3646 (1977).

[CrossRef]

W. C. K. Mak, B. A. Malomed, and P. L. Chu, “Formation of a standing-light pulse through collision of gap solitons,” Phys. Rev. E 68, 026609 (2003).

[CrossRef]

W. Li and A. Smerzi, Phys. Rev. E 70, 016605 (2004).

[CrossRef]

I. M. Merhasin, B. V. Gisin, R. Driben, and B. A. Malomed, “Finite-band solitons in the Kronig-Penney model with the cubic-quintic nonlinearity,” Phys. Rev. E 71, 016613 (2005).

[CrossRef]

W. C. K. Mak, B. A. Malomed, and P. L. Chu, “Interaction of a soliton with a localized gain in a fiber Bragg grating,” Phys. Rev. E 67, 026608 (2003).

[CrossRef]

P. Y. P. Chen, B. A. Malomed, and P. L. Chu, “Trapping Bragg solitons by a pair of defects,” Phys. Rev. E 71, 066601 (2005).

[CrossRef]

D. N. Christodoulides and R. I. Joseph, “Slow Bragg solitons in nonlinear periodic structure,” Phys. Rev. Lett. 62, 1746-1749 (1989).

[CrossRef]
[PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003).

[CrossRef]
[PubMed]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Yu. S. Kivshar, “Controlled generation and steering of spatial gap solitons,” Phys. Rev. Lett. 93, 083905 (2004).

[CrossRef]
[PubMed]

I. V. Barashenkov, D. E. Pelinovsky, and E. V. Zemlyanaya, “Vibrations and oscillatory instabilities of gap solitons,” Phys. Rev. Lett. 80, 5117-5120 (1998).

[CrossRef]

A. De Rossi, C. Conti, and S. Trillo, “Stability, multistability, and wobbling of optical gap solitons,” Phys. Rev. Lett. 81, 85-88 (1998).

[CrossRef]

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627-1630 (1996).

[CrossRef]
[PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. 90, 053902 (2003).

[CrossRef]
[PubMed]

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904 (2004).

[CrossRef]
[PubMed]

W. Chen and D. L. Mills, “Gap solitons and the nonlinear-optical response of superlattices,” Phys. Rev. Lett. 58, 160-163 (1987).

[CrossRef]
[PubMed]

E. A. Ostrovskaya and Yu. S. Kivshar, “Matter-wave gap solitons in atomic band-gap structures,” Phys. Rev. Lett. 90, 160407 (2003).

[CrossRef]
[PubMed]

B. Eiermann, Th. Anker, M. Albiez, M. Taglieber, P. Treutlein, K.-P. Marzlin, and M. K. Oberthaler, “Bright Bose-Einstein gap solitons of atoms with repulsive interaction,” Phys. Rev. Lett. 92, 230401 (2004).

[CrossRef]
[PubMed]

P. G. Kevrekidis, “On a class of discretizations of Hamiltonian nonlinear partial differential equations,” Physica D 183, 68-86 (2003).

[CrossRef]

D. E. Pelinovsky and V. M. Rothos, “Bifurcations of travelling wave solutions in the discrete NLS equations,” Physica D 202, 16-36 (2005).

[CrossRef]

D. B. Duncan, J. C. Eilbeck, H. Feddersen, and J. A. D. Wattis, “Solitons on lattices,” Physica D 68, 1-11 (1993).

[CrossRef]

A. Othonos, “Fiber Bragg gratings,” Rev. Sci. Instrum. 68, 4309-4341 (1997).

[CrossRef]

Yu. I. Voloshchenko, Yu. N. Ryzhov, and V. E. Sotin, “Stationary waves in nonlinear, periodically modulated media with large group retardation,” Zh. Tekh. Fiz. 51, 902 (1981) Yu. I. Voloshchenko, Yu. N. Ryzhov, and V. E. Sotin,[Sov. Phys. Tech. Phys. 26, 541 (1981)].

C. M. de Sterke and J. E. Sipe, “Gap solitons,” in Progress in Optics, E.Wolf, ed. (North-Holland, 1994), Vol. XXXIII, Chap. III, pp. 203-260.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003).

R. Kashyap, Fiber Bragg Gratings (Academic, 1999).

B. A. Malomed, Soliton Management in Periodic Systems (Springer, 2006).

C. Kittel, Introduction to Solid State Physics (Wiley, 1995).

M. J. Ablowitz and H. Segur, Solitons and Inverse Scattering Transform (SIAM, 1981).

[CrossRef]