The focusing Manakov system with nonzero boundary conditions

DOI10.1088/0951-7715/28/9/3101zbMath1330.35406OpenAlexW2274890641MaRDI QIDQ3196554

Gregor Kovačič, Gino Biondini, Daniel K. Kraus

Publication date: 29 October 2015

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/5eaa79bdba30e6b0837ec02896b7cd2e980001ca

zbMATH Keywords

inverse scattering transformintegrabilityRiemann-Hilbert problemsolitonsnonlinear Schrödinger equationsJost eigenfunctions

Mathematics Subject Classification ID

Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) NLS equations (nonlinear Schrödinger equations) (35Q55) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Scattering theory, inverse scattering involving ordinary differential operators (34L25) Soliton solutions (35C08)

Related Items (32)

Focusing and defocusing mKdV equations with nonzero boundary conditions: inverse scattering transforms and soliton interactions ⋮ Manakov system with parity symmetry on nonzero background and associated boundary value problems ⋮ Imaginary eigenvalues of Zakharov-Shabat problems with non-zero background ⋮ Defocusing NLS equation with nonzero background: large-time asymptotics in a solitonless region ⋮ Long-time asymptotics for a mixed nonlinear Schrödinger equation with the Schwartz initial data ⋮ \(l^2\)-Sobolev space bijectivity of the scattering-inverse scattering transforms related to defocusing Ablowitz-Ladik systems ⋮ Riemann–Hilbert approach for discrete sine‐Gordon equation with simple and double poles ⋮ Vector breathers in the Manakov system ⋮ Inverse scattering problem for the matrix modified Korteweg-de Vries equation with finite density type initial data ⋮ The Riemann-Hilbert approach for the higher-order Gerdjikov-Ivanov equation, soliton interactions and position shift ⋮ Three-Wave Interaction Equations: Classical and Nonlocal ⋮ Nonlinear Schrödinger equation with nonzero boundary conditions revisited: Dbar approach ⋮ Universal Nature of the Nonlinear Stage of Modulational Instability ⋮ The Sasa-Satsuma equation on a non-zero background: the inverse scattering transform and multi-soliton solutions ⋮ Inverse scattering transform for nonlinear Schrödinger systems on a nontrivial background: a survey of classical results, new developments and future directions ⋮ Inverse scattering transformation for the \(N\)-component focusing nonlinear Schrödinger equation with nonzero boundary conditions ⋮ Double-pole solutions in the modified nonlinear Schrödinger equation ⋮ Inverse scattering transform and soliton solutions for square matrix nonlinear Schrödinger equations with non-zero boundary conditions ⋮ Large and infinite-order solitons of the coupled nonlinear Schrödinger equation ⋮ Inverse scattering transform for the nonlocal reverse space-time nonlinear Schrödinger equation ⋮ Inverse scattering transforms and soliton solutions of focusing and defocusing nonlocal mKdV equations with non-zero boundary conditions ⋮ Inverse scattering and \(N\)-triple-pole soliton and breather solutions of the focusing nonlinear Schrödinger hierarchy with nonzero boundary conditions ⋮ General soliton solution to a nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions ⋮ Inverse scattering transform for the defocusing nonlinear Schrödinger equation with fully asymmetric non-zero boundary conditions ⋮ The three-component defocusing nonlinear Schrödinger equation with nonzero boundary conditions ⋮ Pure soliton solutions of the nonlocal Kundu-nonlinear Schrödinger equation ⋮ Multi-component nonlinear Schrödinger equations with nonzero boundary conditions: higher-order vector Peregrine solitons and asymptotic estimates ⋮ Reverse Space‐Time Nonlocal Sine‐Gordon/Sinh‐Gordon Equations with Nonzero Boundary Conditions ⋮ Inverse scattering transform for the coupled modified Korteweg-de Vries equation with nonzero boundary conditions ⋮ Inverse scattering transform for two-level systems with nonzero background ⋮ Inverse Scattering Transform for the Defocusing Manakov System with Non-Parallel Boundary Conditions at Infinity ⋮ Riemann-Hilbert approach to the modified nonlinear Schrödinger equation with non-vanishing asymptotic boundary conditions

This page was built for publication: The focusing Manakov system with nonzero boundary conditions