GBDT and algebro-geometric approaches to explicit solutions and wave functions for nonlocal NLS

DOI10.1088/1751-8121/aaedebzbMath1422.35151arXiv1806.05019OpenAlexW3099276793WikidataQ128999769 ScholiaQ128999769MaRDI QIDQ5235187

Johanna Michor, Alexander L. Sakhnovich

Publication date: 7 October 2019

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.05019

zbMATH Keywords

explicit solutionwave functionDarboux matrixBäcklund-Darboux transformationnonlocal nonlinear Schrödinger equationalgebro-geometric solution

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) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Geometric Langlands program (algebro-geometric aspects) (14D24)

Related Items (8)

Long-time asymptotics for the integrable nonlocal focusing nonlinear Schrödinger equation for a family of step-like initial data ⋮ Binary Darboux transformation and new soliton solutions of the focusing nonlocal nonlinear Schrödinger equation ⋮ Global conservative solutions of the nonlocal NLS equation beyond blow-up ⋮ Breather, lump, and interaction solutions to a nonlocal KP system ⋮ Elliptic‐ and hyperbolic‐function solutions of the nonlocal reverse‐time and reverse‐space‐time nonlinear Schrödinger equations ⋮ Focusing nonlocal nonlinear Schrödinger equation with asymmetric boundary conditions: large-time behavior ⋮ General stationary solutions of the nonlocal nonlinear Schrödinger equation and their relevance to the PT-symmetric system ⋮ Defocusing nonlocal nonlinear Schr\"odinger equation with step-like boundary conditions: long-time behavior for shifted initial data

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