Inverse scattering transform for the focusing nonlinear Schrödinger equation with counterpropagating flows

DOI10.1111/sapm.12347zbMath1472.35347arXiv2005.02336OpenAlexW3107367771MaRDI QIDQ4995582

Gino Biondini, Jonathan Lottes, Dionyssios Mantzavinos

Publication date: 25 June 2021

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.02336

zbMATH Keywords

nonlinear wavespartial differential equationssolitons and integrable systems

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) NLS equations (nonlinear Schrödinger equations) (35Q55) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Riemann-Hilbert problems in context of PDEs (35Q15) Soliton solutions (35C08)

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A matrix Schrödinger approach to focusing nonlinear Schrödinger equations with nonvanishing boundary conditions ⋮ A Riemann-Hilbert approach in the form of a block matrix for the coupled matrix integrable system ⋮ Riemann-Hilbert problem for the focusing nonlinear Schrödinger equation with multiple high-order poles under nonzero boundary conditions ⋮ Nonlinear Schrödinger equation with nonzero boundary conditions revisited: Dbar approach ⋮ Inverse scattering transformation for the \(N\)-component focusing nonlinear Schrödinger equation with nonzero boundary conditions ⋮ A Riemann-Hilbert approach to the modified Camassa-Holm equation with step-like boundary conditions ⋮ \(N\)-fold binary Darboux transformation for the \(n\)th-order Ablowitz-Kaup-Newell-Segur system under a pseudo-symmetry hypothesis

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