Inverse scattering transform for the defocusing nonlinear Schrödinger equation with fully asymmetric non-zero boundary conditions

DOI10.1016/j.physd.2016.04.003zbMath1415.35217OpenAlexW2397515279MaRDI QIDQ2000232

Emily Fagerstrom, Barbara Prinari, Gino Biondini

Publication date: 28 June 2019

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

Full work available at URL: https://doi.org/10.1016/j.physd.2016.04.003

zbMATH Keywords

inverse scattering transformintegrable systemsnonlinear Schrödinger equationnonzero boundary conditions

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Scattering theory for PDEs (35P25) NLS equations (nonlinear Schrödinger equations) (35Q55)

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Cites Work

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• Long time behavior for the focusing nonlinear Schrödinger equation with real spectral singularities
• Long-time asymptotics of solutions to the Cauchy problem for the defocusing nonlinear Schrödinger equation with finite-density initial data. II: Dark solitons on continua
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• Solvability of the direct and inverse problems for the nonlinear Schrödinger equation
• The inverse scattering transform for the focusing nonlinear Schrödinger equation with asymmetric boundary conditions
• The Inverse Scattering Transform for the Defocusing Nonlinear Schrödinger Equations with Nonzero Boundary Conditions
• Regularization of a sharp shock by the defocusing nonlinear Schrödinger equation
• Focusing NLS Equation: Long-Time Dynamics of Step-Like Initial Data
• Inverse Scattering Transform for the Multi-Component Nonlinear Schrödinger Equation with Nonzero Boundary Conditions
• The focusing Manakov system with nonzero boundary conditions
• Direct and inverse scattering transforms with arbitrary spectral singularities
• Inverse scattering transform for the vector nonlinear Schrödinger equation with nonvanishing boundary conditions
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• The Perturbed Plane-Wave Solutions of the Cubic Schrödinger Equation
• Large-time continuum asymptotics of dark solitons
• The Riemann–Hilbert Problem and Inverse Scattering
• Robin boundary condition and shock problem for the focusing nonlinear Schrödinger equation
• Inverse Scattering Transform for the Defocusing Manakov System with Nonzero Boundary Conditions
• The Integrable Nature of Modulational Instability
• Long‐time asymptotics of the nonlinear Schrödinger equation shock problem
• Inverse scattering transform for the focusing nonlinear Schrödinger equation with nonzero boundary conditions
• On the Spectrum of the Dirac Operator and the Existence of Discrete Eigenvalues for the Defocusing Nonlinear Schrödinger Equation
• Dark-bright soliton solutions with nontrivial polarization interactions for the three-component defocusing nonlinear Schrödinger equation with nonzero boundary conditions