Integrable nonlocal nonlinear equations

MJ Ablowitz, ZH Musslimani - Studies in Applied Mathematics, 2017 - Wiley Online Library
A nonlocal nonlinear Schrödinger (NLS) equation was recently found by the authors and
shown to be an integrable infinite dimensional Hamiltonian equation. Unlike the classical …

Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation

MJ Ablowitz, ZH Musslimani - Nonlinearity, 2016 - iopscience.iop.org
A nonlocal nonlinear Schrödinger (NLS) equation was recently introduced and shown to be
an integrable infinite dimensional Hamiltonian evolution equation. In this paper a detailed …

Transformations between nonlocal and local integrable equations

B Yang, J Yang - Studies in applied mathematics, 2018 - Wiley Online Library
Recently, a number of nonlocal integrable equations, such as the‐symmetric nonlinear
Schrödinger (NLS) equation and‐symmetric Davey–Stewartson equations, were proposed …

[HTML][HTML] Integrable space-time shifted nonlocal nonlinear equations

MJ Ablowitz, ZH Musslimani - Physics Letters A, 2021 - Elsevier
Abstract In 1974 Ablowitz, Kaup, Newell, Segur (AKNS) put forward a theoretical framework
whereby one can construct evolution equations that are (i) integrable in the sense of …

Solutions of nonlocal equations reduced from the AKNS hierarchy

K Chen, X Deng, S Lou, D Zhang - Studies in Applied …, 2018 - Wiley Online Library
In this paper, nonlocal reductions of the Ablowitz–Kaup–Newell–Suger (AKNS) hierarchy
are collected, including the nonlocal nonlinear Schrödinger hierarchy, nonlocal modified …

Reverse space‐time nonlocal sine‐Gordon/sinh‐Gordon equations with nonzero boundary conditions

MJ Ablowitz, BF Feng, XD Luo… - Studies in Applied …, 2018 - Wiley Online Library
Nonlocal reverse space‐time Sine/Sinh‐Gordon type equations were recently introduced.
They arise from a remarkably simple nonlocal reduction of the well‐known AKNS scattering …

Physically significant nonlocal nonlinear Schrödinger equation and its soliton solutions

J Yang - Physical Review E, 2018 - APS
An integrable nonlocal nonlinear Schrödinger (NLS) equation with clear physical
motivations is proposed. This equation is obtained from a special reduction of the Manakov …

Discrete nonlocal nonlinear Schrödinger systems: Integrability, inverse scattering and solitons

MJ Ablowitz, XD Luo, ZH Musslimani - Nonlinearity, 2020 - iopscience.iop.org
A number of integrable nonlocal discrete nonlinear Schrödinger (NLS) type systems have
been recently proposed. They arise from integrable symmetry reductions of the well-known …

Binary Darboux transformation of vector nonlocal reverse-time integrable NLS equations

WX Ma - Chaos, Solitons & Fractals, 2024 - Elsevier
The aim of this paper is to study vector nonlocal reverse-time NLS (nonlinear Schrödinger)
equations and present a binary Darboux transformation by utilizing two sets of …

Integrable multidimensional versions of the nonlocal nonlinear Schrödinger equation

AS Fokas - Nonlinearity, 2016 - iopscience.iop.org
Two new integrable nonlocal Davey–Stewartson equations are introduced. These equations
provide two-spatial dimensional analogues of the integrable, nonlocal nonlinear Schrö …