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High-Order-Mode Soliton Structures in Two-Dimensional Lattices with Defocusing Nonlinearity

P. G. Kevrekidis·H. Susanto·Z. Chen
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Abstract

While fundamental-mode discrete solitons have been demonstrated with both self-focusing and defocusing nonlinearity, high-order-mode localized states in waveguide lattices have been studied thus far only for the self-focusing case. In this paper, the existence and stability regimes of dipole, quadrupole and vortex soliton structures in two-dimensional lattices induced with a defocusing nonlinearity are examined by the theoretical and numerical analysis of a generic envelope nonlinear lattice model. In particular, we find that the stability of such high-order-mode solitons is quite different from that with self-focusing nonlinearity. As a simple example, a dipole (``twisted'') mode soliton which may be stable in the focusing case becomes unstable in the defocusing regime. Our results may be relevant to other two-dimensional defocusing periodic nonlinear systems such as Bose-Einstein condensates with a positive scattering length trapped in optical lattices.

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P. G. Kevrekidis, H. Susanto, Z. Chen. 2006-10-27. High-Order-Mode Soliton Structures in Two-Dimensional Lattices with Defocusing Nonlinearity. https://doi.org/10.1103/physreve.74.066606

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