It is commonly known that the interplay of linear and nonlinear effects gives rise to solitons, i.e., self-trapped localized structures, in a wide range of physical settings, including optics, Bose-Einstein condensates (BECs), hydrodynamics, plasmas, condensed-matter physics, etc. Nowadays, solitons are considered as an interdisciplinary class of modes, which feature diverse internal structures.
While most experimental realizations and theoretical models of solitons have been elaborated in one-dimensional (1D) settings, a challenging issue is prediction of stable solitons in 2D and 3D media. In particular, multidimensional solitons may carry an intrinsic topological structure in the form of vorticity. In addition to the "simple" vortex solitons, fascinating objects featuring complex structures, such as hopfions, i.e., vortex rings with internal twist, have been predicted too.
A fundamental problem is the propensity of multidimensional solitons to be unstable (naturally, solitons with a more sophisticated structure, such as vortex solitons, are more vulnerable to instabilities). Recently, novel perspectives for the creation of stable 2D and 3D solitons were brought to the attention of researchers in optics and BEC. The present talk aims to provide an overview of the main results and ongoing developments in this vast field. An essential conclusion is the benefit offered by the exchange of concepts between different areas, such as optics, BEC, and hydrodynamics.
A thorough survey of the topic is provided in a new book: B. A. Malomed, "Multidimensional Solitons" (American Institute of Physics, Melville, NY, 2022).
Recent review articles on the subject are available too:
Y. Kartashov, G. Astrakharchik, B. Malomed, and L. Torner, Frontiers in multidimensional self-trapping of nonlinear fields and matter, Nature Reviews Physics 1, 185-197 (2019) https://doi.org/10.1038/s42254-019-0025-7.
B. A. Malomed, (INVITED) Vortex solitons: Old results and new perspectives, Physica D 399, 108-137 (2019) https://doi.org/10.1016/j.physd.2019.04.009 free access: https://authors.elsevier.com/a/1ZXATc2Eea3QG
Z. Luo, W. Pang, B. Liu, Y. Li, and B. A. Malomed, A new form of liquid matter: quantum droplets, Front. Phys. 16, 32501 (2021) https://link.springer.com/article/10.1007/s11467-020-1020-2.
B. A. Malomed, Multidimensional dissipative solitons and solitary vortices, Chaos, Solitons & Fractals 163, 112526 (2022) https://doi.org/10.1016/j.chaos.2022.112526.