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Discrete and Semi-discrete Multidimensional Solitons and Vortices: Established Results and Novel Findings
Version 1
: Received: 8 January 2024 / Approved: 8 January 2024 / Online: 9 January 2024 (02:30:13 CET)
A peer-reviewed article of this Preprint also exists.
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. 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.
Keywords
Nonlinear optics; Bose-Einstein condensates; lattice dynamics; nonlinear Schrödinger equations; vortices; skyrmions; Salerno model; spin-orbit coupling; quantum droplets; PT symmetry
Subject
Physical Sciences, Theoretical Physics
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.
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