2007
DOI: 10.1103/physreve.76.066604
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Cubic-quintic solitons in the checkerboard potential

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 branc… Show more

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Cited by 38 publications
(30 citation statements)
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“…Solitons can also be found in finite bandgaps; however, as well as in the 2D KP model with the self-repulsive χ (5) term [13], all gap solitons turn out to be unstable.…”
Section: Fundamental and Multi-humped Solitonsmentioning
confidence: 99%
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“…Solitons can also be found in finite bandgaps; however, as well as in the 2D KP model with the self-repulsive χ (5) term [13], all gap solitons turn out to be unstable.…”
Section: Fundamental and Multi-humped Solitonsmentioning
confidence: 99%
“…Subsequent derivation of the VA from Lagrangian (5) and ansatz (6) is straightforward for the cos potential. In the KP model, the checkerboard potential may be replaced, for this purpose, by its two lowest spatial harmonics [13]. Thus, the calculation of the respective effective Lagrangian, L = L (Q, W ), leads to the variational equations, ∂L/∂Q = ∂L/∂W = 0, which take the form of…”
Section: Fundamental and Multi-humped Solitonsmentioning
confidence: 99%
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“…In this context, a conjecture that would be worthwhile proving is that, in an infinite periodic lattice formed by potential wells, the nonlinearity can support 2D solitons and localized vortices with various symmetries, but not confined asymmetric states. This conjecture is suggested by results reported for infinite linear [31] and nonlinear [32] potential lattices.…”
Section: Discussionmentioning
confidence: 62%