## Coupled-Mode Equations and Gap Solitons in a Two-Dimensional Nonlinear Elliptic Problem with a Separable Periodic Potential

- Tomás Dohnal, Dmitry E Pelinovsky, Guido Schneider
- J. Nonlinear Science
- 2009

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@article{Shi2007SolitaryWB, title={Solitary waves bifurcated from Bloch-band edges in two-dimensional periodic media.}, author={Zuoqiang Shi and Jianke Yang}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2007}, volume={75 5 Pt 2}, pages={056602} }

- Published 2007 in Physical review. E, Statistical, nonlinear, and…

Solitary waves bifurcated from edges of Bloch bands in two-dimensional periodic media are determined both analytically and numerically in the context of a two-dimensional nonlinear Schrödinger equation with a periodic potential. Using multiscale perturbation methods, the envelope equations of solitary waves near Bloch bands are analytically derived. These envelope equations reveal that solitary waves can bifurcate from edges of Bloch bands under either focusing or defocusing nonlinearity… CONTINUE READING