Malomed, B.A. Discrete and Semi-Discrete Multidimensional Solitons and Vortices: Established Results and Novel Findings. Entropy2024, 26, 137.
Malomed, B.A. Discrete and Semi-Discrete Multidimensional Solitons and Vortices: Established Results and Novel Findings. Entropy 2024, 26, 137.
Malomed, B.A. Discrete and Semi-Discrete Multidimensional Solitons and Vortices: Established Results and Novel Findings. Entropy2024, 26, 137.
Malomed, B.A. Discrete and Semi-Discrete Multidimensional Solitons and Vortices: Established Results and Novel Findings. Entropy 2024, 26, 137.
Abstract
This article presents a concise survey of basic discrete and semi-discrete nonlinear models which produce two- and three-dimensional (2D and 3D) solitons, and a summary of main theoretical and experimental results obtained for such solitons. The models are based on the discrete nonlinear Schrödinger (DNLS) equations and their generalizations, such as a system of discrete Gross-Pitaevskii (GP) equations with the Lee-Huang-Yang corrections, the 2D Salerno model (SM), DNLS equations with long-range dipole-dipole and quadrupole-quadrupole interactions, a system of coupled discrete equations for the second-harmonic generation with the quadratic (χ⁽²⁾) nonlinearity, a 2D DNLS equation with a superlattice modulation opening mini-gaps, a discretized NLS equation with rotation, a DNLS coupler and its PT-symmetric version, a system of DNLS equations for the spin-orbit-coupled (SOC) binary Bose-Einstein condensate, and others. The article presents a review of basic species of multidimensional discrete modes, including fundamental and vortex solitons, their bound states, gap solitons populating mini-gaps, symmetric and asymmetric solitons in the conservative and PT-symmetric couplers, cuspons in the 2D SM, discrete SOC solitons of the semi-vortex and mixed-mode types, 3D discrete skyrmions, and some others.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
