Band Gap Formation, Fundamental Solitons and Vortices in Two Dimensional Lattices

Localized nonlinear modes in systems with periodic potentials have recently attracted considerable interest. We discuss the existence of fundamental solitons and the band gap structures in two dimensional lattices. In the current study,  two dimensional lattices, possesing dislocations, defects and quasicrystal structures are considered. The existence of localized vortices in two dimensional media governed by the cubic NLS equation with external periodic and Penrose potentials are investigated.
 

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