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ABSTRACT
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.
Acronyms
| 1D | = | one-dimensional |
| 2D | = | two-dimensional |
| 3D | = | three-dimensional |
| BEC | = | Bose-Einstein condensate |
| CQ | = | cubic-quintic (nonlinearity)) |
| FT | = | flat-top (profiles of solitons and quantum droplets) |
| GP | = | Gross-Pitaevskii (equation) |
| GS | = | ground state |
| GVD | = | group-velocity dispersion |
| LHY | = | Lee-Huang-Yang (correction to the MF theory) |
| MF | = | mean-field (approximation) |
| NLS | = | nonlinear Schr¨odinger (equation) |
| QD | = | quantum droplet |
| SOC | = | spin-orbit coupling |
| STOV | = | spatiotemporal vortex |
| TS | = | Townes soliton |
| VA | = | variational approximation |
| VK | = | Vakhitov-Kolokolov (stability criterion) |
| ZS | = | Zeeman splitting |
Acknowledgments
I would like to thank my colleagues, with whom I collaborated on topics addressed in this review: F. Kh. Abdullaev, D. Anderson, G. Astrakharchik, C. B. de Araújo, B. B. Baizakov, W. B. Cardoso, G. Dong, N. Dror, P. D. Drummond, A. Gammal, Y. V. Kartashov, V. V. Konotop, H. Leblond, B. Li, Y. Li, M. Lisak, Z.-H. Luo, D. Mihalache, M. Modugno, W. Pang, M. A. Porras, H. Pu, J. Qin, A. S. Reyna, H. Sakaguchi, L. Salasnich, M. Salerno, E. Ya. Sherman, V. Skarka, D. V. Skryabin, L. Tarruell, L. Torner, F. Wise, L. G. Wright, and J. Zeng. I also thank Editors of Advances in Physics X, J. S. Aitchison, N. Balmforth, and R. Palmer, for their invitation to write this review article. My work on this topic was partly supported by the Israel Science Foundation through grant No. 1695/22.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Notes
1. Sabbatical address.