Discrete and semi-discrete multidimensional solitons and vortices: Established results and novel findings

Fuente: arXiv
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Main Author: Malomed, Boris A.
Format: Preprint
Published: 2024
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author Malomed, Boris A.
author_facet Malomed, Boris A.
contents 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 Schroeodinger (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 (chi^(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 condensates, and others. The article presents a review of basic species of multidimensional discrete modes, including fundamental (zero-vorticity) 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.
format Preprint
id arxiv_https___arxiv_org_abs_2401_16550
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Discrete and semi-discrete multidimensional solitons and vortices: Established results and novel findings
Malomed, Boris A.
Pattern Formation and Solitons
Quantum Gases
Optics
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 Schroeodinger (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 (chi^(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 condensates, and others. The article presents a review of basic species of multidimensional discrete modes, including fundamental (zero-vorticity) 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.
title Discrete and semi-discrete multidimensional solitons and vortices: Established results and novel findings
topic Pattern Formation and Solitons
Quantum Gases
Optics
url https://arxiv.org/abs/2401.16550