Inverse scattering transforms and soliton solutions of focusing and defocusing nonlocal mKdV equations with non-zero boundary conditions

DOI10.1016/j.physd.2019.132170zbMath1453.37069arXiv1810.12143OpenAlexW2969475408WikidataQ127338675 ScholiaQ127338675MaRDI QIDQ2222726

Zhenya Yan, Guoqiang Zhang

Publication date: 27 January 2021

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.12143

zbMATH Keywords

inverse scattering transformsolitonsRiemann surfacematrix Riemann-Hilbert problemnonzero boundary conditionsnonlocal modified KdV equation

Mathematics Subject Classification ID

Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15)

Related Items (37)

Inverse scattering transforms for the nonlocal Hirota–Maxwell–Bloch system ⋮ Double and triple pole solutions for the Gerdjikov–Ivanov type of derivative nonlinear Schrödinger equation with zero/nonzero boundary conditions ⋮ Focusing and defocusing mKdV equations with nonzero boundary conditions: inverse scattering transforms and soliton interactions ⋮ \(N\)-double poles solutions for nonlocal Hirota equation with nonzero boundary conditions using Riemann-Hilbert method and PINN algorithm ⋮ Darboux transformation and exact solutions of the variable coefficient nonlocal Newell-Whitehead equation ⋮ Inverse scattering transform for the integrable nonlocal Lakshmanan-Porsezian-Daniel equation ⋮ Binary Darboux transformation for the Gerdjikov-Ivanov equation ⋮ Soliton and breather solutions for a fifth-order modified KdV equation with a nonzero background ⋮ The general fifth-order nonlinear Schrödinger equation with nonzero boundary conditions: inverse scattering transform and multisoliton solutions ⋮ Riemann-Hilbert problem for the focusing nonlinear Schrödinger equation with multiple high-order poles under nonzero boundary conditions ⋮ Solitary wave solutions and integrability for generalized nonlocal complex modified Korteweg-de Vries (cmKdV) equations ⋮ Solutions to integrable space-time shifted nonlocal equations ⋮ Inverse scattering transforms of the inhomogeneous fifth-order nonlinear Schrödinger equation with zero/nonzero boundary conditions ⋮ Solutions to the complex shifted reverse space-time modified Korteweg-de Vries equation ⋮ Exact solutions and Darboux transformation for the reverse space-time nonlocal Lakshmanan-Porsezian-Daniel equation ⋮ Large‐time asymptotics to the focusing nonlocal modified Kortweg‐de Vries equation with step‐like boundary conditions ⋮ Soliton and breather solutions of the higher-order modified Korteweg-de Vries equation with constants background ⋮ Breather solutions to the AB system with non-zero background ⋮ Long time asymptotic behavior for the nonlocal mKdV equation in solitonic space-time regions ⋮ Inverse scattering transform and dynamics of soliton solutions for nonlocal focusing modified Korteweg-de Vries equation ⋮ Nonlinear Schrödinger equation with nonzero boundary conditions revisited: Dbar approach ⋮ Riemann–Hilbert approach to the focusing and defocusing nonlocal complex modified Korteweg–de Vries equation with step-like initial data ⋮ Double-pole solutions in the modified nonlinear Schrödinger equation ⋮ Interaction solutions of the \((2+1)\)-dimensional Sawada-Kotera equation ⋮ Multi-place physics and multi-place nonlocal systems ⋮ Integrability, Darboux transformation and exact solutions for nonlocal couplings of AKNS equations ⋮ Inverse scattering and \(N\)-triple-pole soliton and breather solutions of the focusing nonlinear Schrödinger hierarchy with nonzero boundary conditions ⋮ On \((2+1)\)-dimensional mixed AKNS hierarchy ⋮ On a Riemann-Hilbert problem for the focusing nonlocal mKdV equation with step-like initial data ⋮ The derivative nonlinear Schrödinger equation with zero/nonzero boundary conditions: inverse scattering transforms and \(N\)-double-pole solutions ⋮ The Riemann-Hilbert approach for the focusing Hirota equation with single and double poles ⋮ Pure soliton solutions of the nonlocal Kundu-nonlinear Schrödinger equation ⋮ Long-time asymptotics for the focusing Hirota equation with non-zero boundary conditions at infinity via the Deift-Zhou approach ⋮ Inverse scattering transform for the coupled modified Korteweg-de Vries equation with nonzero boundary conditions ⋮ Inverse scattering transform of an extended nonlinear Schrödinger equation with nonzero boundary conditions and its multisoliton solutions ⋮ Soliton solutions of the shifted nonlocal NLS and MKdV equations ⋮ Long time asymptotics for the nonlocal mKdV equation with finite density initial data

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