Multidimensional solitons: Well-established results and novel findings
Boris A. Malomed

TL;DR
This paper reviews well-known and recent results on 2D and 3D multidimensional solitons, focusing on their stability, physical realizations, and recent stabilization methods involving harmonic traps and spin-orbit coupling.
Contribution
It provides a comprehensive review of stabilization techniques for multidimensional solitons, including new approaches for free-space solitons with spin-orbit coupling.
Findings
Stabilization of 2D and 3D solitons in harmonic-oscillator potentials.
Existence of metastable 3D solitons without a true ground state.
Different stabilization mechanisms in 2D and 3D geometries.
Abstract
A brief review is given of some well-known and some very recent results obtained in studies of two- and three-dimensional (2D and 3D) solitons. Both zero-vorticity (fundamental) solitons and ones carrying vorticity S = 1 are considered. Physical realizations of multidimensional solitons in atomic Bose-Einstein condensates (BECs) and nonlinear optics are briefly discussed too. Unlike 1D solitons, which are typically stable, 2D and 3D ones are vulnerable to instabilities induced by the occurrence of the critical and supercritical collapse, respectively, in the same 2D and 3D models that give rise to the solitons. Vortex solitons are subject to a still stronger splitting instability. For this reason, a central problem is search for physical settings in which 2D and 3D solitons may be stabilized. The brief review addresses one well-established topic, viz., the stabilization of the 3D and 2D…
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