PMID:18233934

Citation	Driben, R, Malomed, BA, Gubeskys, A and Zyss, J (2007) Cubic-quintic solitons in the checkerboard potential. Phys Rev E Stat Nonlin Soft Matter Phys 76:066604
Abstract	We introduce a two-dimensional (2D) model which combines a checkerboard potential, alias the Kronig-Penney (KP) lattice, with the self-focusing cubic and self-defocusing quintic nonlinear terms. The beam-splitting mechanism and soliton multistability are explored in this setting, following the recently considered 1D version of the model. Families of single- and multi-peak solitons (in particular, five- and nine-peak species naturally emerge in the 2D setting) are found in the semi-infinite gap, with both branches of bistable families being robust against perturbations. For single-peak solitons, the variational approximation (VA) is developed, providing for a qualitatively correct description of the transition from monostability to the bistability. 2D solitons found in finite band gaps are unstable. Also constructed are two different species of stable vortex solitons, arranged as four-peak patterns ("oblique" and "straight" ones). Unlike them, compact "crater-shaped" vortices are unstable, transforming themselves into randomly walking fundamental beams.
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