Localized modes of the (n+1)-dimensional Schrödinger equation with power-law nonlinearities in \(\mathcal{PT}\)-symmetric potentials

DOI10.1016/j.cnsns.2016.07.002zbMath1466.35324OpenAlexW2469586248MaRDI QIDQ2005008

Chao-Qing Dai, Yan Fan, Xiao-Fei Zhang, Liang Chen

Publication date: 7 October 2020

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2016.07.002

zbMATH Keywords

power-law nonlinearitylocalized modes\(\mathcal{PT}\)-symmetric potential(n+1)-dimensional nonlinear Schrödinger equationsstability,

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton solutions (35C08)

Related Items (13)

Solitons supported by competing nonlinearity, higher order dispersion and \(\mathcal{PT}\)-symmetric potential ⋮ Stable solitons in the 1D and 2D generalized nonlinear Schrödinger equations with the periodic effective mass and \(\mathcal{PT}\)-symmetric potentials ⋮ Breather wave solutions for the generalized shallow water wave equation with variable coefficients in the atmosphere, rivers, lakes and oceans ⋮ One- and two-dimensional gap solitons and dynamics in the \(\mathcal{PT}\)-symmetric lattice potential and spatially-periodic momentum modulation ⋮ Multi-dimensional stable fundamental solitons and excitations in \(\mathcal{PT}\)-symmetric harmonic-Gaussian potentials with unbounded gain-and-loss distributions ⋮ Effect of power-law nonlinearity on ${ \mathcal P }{ \mathcal T }$-symmetric optical system with fourth-order diffraction ⋮ Lie symmetry analysis and dynamic behaviors for nonlinear generalized Zakharov system ⋮ Stable flat-top solitons and peakons in the PT-symmetric δ -signum potentials and nonlinear media ⋮ Interaction behaviors for the \((2+1)\)-dimensional Sawada-Kotera equation ⋮ Higher-dimensional soliton generation, stability and excitations of the \(\mathcal{PT}\)-symmetric nonlinear Schrödinger equations ⋮ Bright soliton dynamics in higher-dimensional system with power-law nonlinearity ⋮ INTERACTION SOLUTIONS AND ABUNDANT EXACT SOLUTIONS FOR THE NEW (3+1)-DIMENSIONAL GENERALIZED KADOMTSEV-PETVIASHVILI EQUATION IN FLUID MECHANICS ⋮ EXPLICIT AND EXACT NON-TRAVELING WAVE SOLUTIONS OF (3+1)-DIMENSIONAL GENERALIZED SHALLOW WATER EQUATION

Cites Work

• Controllable behaviors of spatiotemporal breathers in a generalized variable-coefficient nonlinear Schrödinger model from arterial mechanics and optical fibers
• Control and management of the combined Peregrine soliton and Akhmediev breathers in \({\mathcal{PT}}\)-symmetric coupled waveguides
• Spatiotemporal Hermite-Gaussian solitons of a (3 + 1)-dimensional partially nonlocal nonlinear Schrödinger equation
• Soliton solution and bifurcation analysis of the Zakharov-Kuznetsov-Benjamin-Bona-Mahoney equation with power law nonlinearity
• Observation of two soliton propagation in an erbium doped inhomogeneous lossy fiber with phase modulation
• Nonlinear localized modes in \(\mathcal{PT}\)-symmetric optical media with competing gain and loss
• Soliton excitations and shape-changing collisions in alpha helical proteins with interspine coupling at higher order
• Exact solutions for a Wick-type stochastic reaction Duffing equation
• Analytical solutions to a class of nonlinear Schrödinger equations with {\cal PT} -like potentials
• Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry

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