Multidimensional soliton systems

• Published in: Advances in physics: X Vol. 9; no. 1
• Main Author: Malomed, Boris A.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 31.12.2024; Taylor & Francis Ltd; Taylor & Francis Group
• Subjects: Approximation; Bose-Einstein condensates; Catastrophic collapse; Compressive strength; Longitudinal waves; nonlinear optics; Orbital stability; Physics; quantum droplets; Solitary waves; spin-orbit coupling; Spin-orbit interactions; Splitting; stability; Toruses; Vortex rings; Vortices; Vorticity
• ISSN: 2374-6149; 2374-6149
• DOI: 10.1080/23746149.2023.2301592

This concise review aims to provide a summary of the most relevant recent experimental and theoretical results for solitons, i.e. self-trapped bound states of nonlinear waves, in two- and three-dimensional (2D and 3D) media. In comparison with commonly known one-dimensional solitons, which are, normally, stable modes, a challenging problem is the propensity of 2D and 3D solitons to instability, caused by the occurrence of the critical or supercritical wave collapse (catastrophic self-compression) in the same spatial dimensions. A remarkable feature of multidimensional solitons is their ability to carry vorticity; however, 2D vortex rings and 3D vortex tori are subject to a strong splitting instability. Therefore, it is natural to categorize the basic results according to physically relevant settings which make it possible to stabilize fundamental (non-topological) and vortex solitons against the collapse and splitting, respectively. The present review is focused on schemes that were recently elaborated in terms of Bose-Einstein condensates and similar photonic setups. These are two-component systems with spin-orbit coupling, and ones stabilized by the beyond-mean-field Lee-Huang-Yang effect. The latter setting has been implemented experimentally, giving rise to stable self-trapped quasi-2D and 3D quantum droplets. Characteristic examples of stable three-dimensional solitons: a semi-vortex (top) and mixed-mode (bottom) modes in the binary Bose-Einstein condensate, stabilized by the spin-orbit coupling.