On multidimensional solitons and their legacy in contemporary Atomic, Molecular and Optical physics

@article{Malomed2016OnMS,
  title={On multidimensional solitons and their legacy in contemporary Atomic, Molecular and Optical physics},
  author={Boris A. Malomed and Lluis Torner and Frank W. Wise and Dumitru Mihalache},
  journal={Journal of Physics B: Atomic, Molecular and Optical Physics},
  year={2016},
  volume={49}
}
This viewpoint relates to an article by B A Malomed, D Mihalache, F Wise, and L Torner (2005 J. Opt. B: Quantum Semiclass. Opt. 7 R53–R72) and was published as part of a series of viewpoints celebrating 50 of the most influential papers published in the Journal of Physics series, which is celebrating its 50th anniversary. 
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86 Citations
Highly Influential Citations
1
Background Citations
3

86 Citations

Multiple-soliton solutions and a generalized double Wronskian determinant to the ( + )-dimensional nonlinear Schrödinger equations
is a well-known mathematical model for describing the evolution of pulses in nonlinear optical fibers and of surface gravity waves in fluid dynamics []. To investigate different complex nonlinear…
Frontiers in multidimensional self-trapping of nonlinear fields and matter
Abstract2D and 3D solitons and related states, such as quantum droplets, can appear in optical systems, atomic Bose–Einstein condensates (BECs) and liquid crystals, among other physical settings.…
Multiple-soliton solutions and a generalized double Wronskian determinant to the (2+1)$(2+1)$-dimensional nonlinear Schrödinger equations
A (2+1)$(2+1)$-dimensional nonlinear Schrödinger equation is mainly discussed. Based on the Hirota direct method and the Wronskian technique, multiple-soliton solutions and a generalized double…
Two-Dimensional Solitons in Nonlocal Media: A Brief Review
This is a review addressing soliton-like states in systems with nonlocal nonlinearity. The work on this topic has long history in optics and related areas. Some results produced by the work (such as…
Interactions of three-dimensional solitons in the cubic-quintic model.
We report results of a systematic numerical analysis of interactions between three-dimensional (3D) fundamental solitons, performed in the framework of the nonlinear Schrödinger equation (NLSE) with…
Vortex dynamics of counterpropagting laser beams in photorefractive materials
We study vortex patterns of counterpropagating laser beams in a photorefractive crystal, with or without the background photonic lattice. The vortices are effectively planar and have two “flavors”…
Soliton lattices in the Gross–Pitaevskii equation with nonlocal and repulsive coupling
N-Fold Darboux Transformation for the Classical Three-Component Nonlinear Schrödinger Equations and Its Exact Solutions
In this paper, by using the gauge transformation and the Lax pairs, the N-fold Darboux transformation (DT) of the classical three-component nonlinear Schrodinger (NLS) equations is given. In…
(INVITED) Vortex solitons: Old results and new perspectives
  • B. Malomed
  • Physics
    Physica D: Nonlinear Phenomena
  • 2019
Suppression of the critical collapse for one-dimensional solitons by saturable quintic nonlinear lattices.
TLDR
It is demonstrated that this purpose can be achieved by combining a nonlinear lattice and saturation of the quintic nonlinearity, which supports three species of solitons, namely, fundamental (even-parity) ones and dipole (odd-Parity) modes of on- and off-site-centered types.
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TLDR
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