Stable 2D localized modes in anisotropic media with harmonic and \(\mathcal{PT}\)-symmetric potentials
type: Item
instance of: scholarly article
title: Stable 2D localized modes in anisotropic media with harmonic and \(\mathcal{PT}\)-symmetric potentials
zbMATH Open document ID: 1341.78016
author: Yixiang Chen
published in: Communications in Nonlinear Science and Numerical Simulation
publication date: 2016-01-26T00:00:00Z
review text: This paper is concerned with analytical spatial localized mode solutions of a two-dimensional nonlinear Schrödinger equation and the corresponding linear stability of these solutions. The nonlinear Schrödinger equation discussed has constant diffraction and nonlinearity in \(\mathcal{PT}\)-symmetric potential. The results show that spatial solitons in a 2D complex \(\mathcal{PT}\)-symmetric Rosen-Morse potential are unstable, and spatial solitons in the \(\mathcal{PT}\)-symmetric potentials with \(m=1,2,3\) are stable in the self-focusing medium while unstable in the self-defocusing medium. Also, the analytical spatial localized mode solutions in anisotropic media with harmonic and \(\mathcal{PT}\)-symmetric potentials are derived based on the relation between two nonlinear Schrödinger equations with variable and constant diffraction and nonlinearity. At last, the diffraction management of spatial localized modes in \(\mathcal{PT}\)-symmetric complex potentials is investigated, and direct numerical simulations are performed to demonstrate their results.
reviewed by: Hongpeng Sun
Mathematics Subject Classification ID: 78A45
Mathematics Subject Classification ID: 78A40
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35C08
zbMATH DE Number: 6535642
zbMATH Keywords: nonlinear Schrödinger equation
zbMATH Keywords: 2D spatial localized modes
zbMATH Keywords: \(\mathcal{PT}\)-symmetric potential
zbMATH Keywords: anisotropic medium
MaRDI profile type: Publication
full work available at URL: j.cnsns.2014.07.027
OpenAlex ID: W1991773740
cites work: Soliton solution and bifurcation analysis of the Zakharov-Kuznetsov-Benjamin-Bona-Mahoney equation with power law nonlinearity
cites work: Notes on the equivalence of different variable separation approaches for nonlinear evolution equations
cites work: Novel rogue waves in an inhomogenous nonlinear medium with external potentials
cites work: Observation of two soliton propagation in an erbium doped inhomogeneous lossy fiber with phase modulation
cites work: Superposed Akhmediev breather of the \({(3+1)}\)-dimensional generalized nonlinear Schrödinger equation with external potentials
cites work: Real Spectra in Non-Hermitian Hamiltonians Having P T Symmetry
cites work: Nonlinear localized modes in \(\mathcal{PT}\)-symmetric optical media with competing gain and loss
cites work: Q3661894
DOI: 10.1016/J.CNSNS.2014.07.027
description: scientific article; zbMATH DE number 6535642