Darboux transformation and explicit solutions for \(2 + 1\)-dimensional nonlocal Schrödinger equation

DOI10.1016/j.aml.2018.12.014zbMath1417.35186OpenAlexW2909885546MaRDI QIDQ1739398

Yan Zhang, Yin-Ping Liu

Publication date: 26 April 2019

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2018.12.014

zbMATH Keywords

solitonDarboux transformationperiodic wavecomplexion solution

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Soliton solutions (35C08)

Related Items (5)

Binary Darboux transformation, solitons, periodic waves and modulation instability for a nonlocal Lakshmanan-Porsezian-Daniel equation ⋮ Exact and approximate solutions for the fractional Schrödinger equation with variable coefficients ⋮ A coupled \((2+1)\)-dimensional mKdV system and its nonlocal reductions ⋮ Inverse scattering transform in two spatial dimensions for the \(N\)-wave interaction problem with a dispersive term ⋮ Darboux transformation and explicit solutions for the \((2 + 1)\)-dimensional nonlocal nonlinear Schrödinger-Maxwell-Bloch system

Cites Work

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• Reductions of Darboux transformations for the \(\mathcal{PT}\)-symmetric nonlocal Davey-Stewartson equations
• Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation
• Faster than Hermitian Quantum Mechanics
• Wave solutions of a (2+1)-dimensional generalization of the nonlinear Schr dinger equation
• Singularity structure analysis and bilinear form of a (2+1) dimensional non-linear Schrodinger (NLS) equation
• 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
• Physical realization of -symmetric potential scattering in a planar slab waveguide
• Some integrable hierarchies in (2+1) dimensions and their twistor description

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