Cauchy matrix type solutions for the nonlocal nonlinear Schrödinger equation

DOI10.1016/S0034-4877(19)30070-9zbMath1441.35218OpenAlexW2968212549MaRDI QIDQ2194258

Wei Feng, Song-Lin Zhao

Publication date: 25 August 2020

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0034-4877(19)30070-9

zbMATH Keywords

reductionsAKNS equationCauchy matrix type solutionslocal and nonlocal nonlinear Schrödinger equation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (10)

Solutions to integrable space-time shifted nonlocal equations ⋮ Solutions and continuum limits to nonlocal discrete sine‐Gordon equations: Bilinearization reduction method ⋮ Integrability of the vector nonlinear Schrödinger-Maxwell-Bloch equation and the Cauchy matrix approach ⋮ Cauchy matrix structure and solutions of the spin-1 Gross-Pitaevskii equations ⋮ A study of periodic solutions and periodic background solutions for the reverse-space-time modified nonlinear Schrödinger equation ⋮ Cauchy matrix solutions to some local and nonlocal complex equations ⋮ Soliton solutions to the nonlocal non-isospectral nonlinear Schrödinger equation ⋮ Multi-place physics and multi-place nonlocal systems ⋮ On \((2+1)\)-dimensional mixed AKNS hierarchy ⋮ Solutions to nonlocal nonisospectral (2 + 1)-dimensional breaking soliton equations

Cites Work

• Darboux transformation and analytic solutions of the discrete \(\mathcal{PT}\)-symmetric nonlocal nonlinear Schrödinger equation
• Integrable \(\mathcal{PT}\)-symmetric local and nonlocal vector nonlinear Schrödinger equations: a unified two-parameter model
• Solutions of the nonlocal nonlinear Schrödinger hierarchy via reduction
• The Sylvester equation and integrable equations: the Ablowitz-Kaup-Newell-Segur system
• Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation
• Nonlocal nonlinear Schrödinger equation and its discrete version: Soliton solutions and gauge equivalence
• Solutions to ABS Lattice Equations via Generalized Cauchy Matrix Approach
• The Sylvester equation and integrable equations: I. The Korteweg-de Vries system and sine-Gordon equation
• Solutions of Nonlocal Equations Reduced from the AKNS Hierarchy

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