Scattering and inverse scattering for first-order systems: II

DOI10.1088/0266-5611/3/4/009zbMath0663.35054OpenAlexW2048840233MaRDI QIDQ3812650

Ronald R. Coifman, Richard W. Beals

Publication date: 1987

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0266-5611/3/4/009

zbMATH Keywords

nonlinear equationseigenfunction expansionfirst-order systemsDarboux transformnonlinear evolutionsdirect and inverse scattering problems

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Nonlinear first-order PDEs (35F20)

Related Items (28)

Second order evolution equations which describe pseudospherical surfaces ⋮ Inverse problem for the Rayleigh system with spectral data ⋮ Inverse scattering on the half-line for ZS-AKNS systems with integrable potentials ⋮ Long-time asymptotics for the pure radiation solution of the sine—gordon equation ⋮ Local isometric immersions of pseudospherical surfaces described by evolution equations in conservation law form ⋮ Poisson commuting energies for a system of infinitely many bosons ⋮ Bäcklund Transformations and Inverse Scattering Solutions for Some Pseudospherical Surface Equations ⋮ Differential Galois theory and Darboux transformations for integrable systems ⋮ Solvability of the derivative nonlinear Schrödinger equation and the massive Thirring model ⋮ Remarks on undecidability, incompleteness and the integrability problem ⋮ On the Dissipative Evolution Equations Associated with the Zakharov-Shabat System with a Quadratic Spectral Parameter ⋮ On the Caudrey-Beals-Coifman System and the Gauge Group Action ⋮ Completeness of the eigenfunctions for the Caudrey–Beals–Coifman system ⋮ \(l^2\)-Sobolev space bijectivity of the scattering-inverse scattering transforms related to defocusing Ablowitz-Ladik systems ⋮ Three-Wave Interaction Equations: Classical and Nonlocal ⋮ A class of third order quasilinear partial differential equations describing spherical or pseudospherical surfaces ⋮ Boundary value problems for the \(N\)-wave interaction equations ⋮ Integrability and a new breed of solitons of an NLS type equation in \(2+1\) dimensions ⋮ Modified Manakov system with self-consistent source. ⋮ Equations of pseudo-spherical type (After S. S. Chern and K. Tenenblat) ⋮ Semiclassical soliton ensembles for the three-wave resonant interaction equations ⋮ Correspondence theorems for hierarchies of equations of pseudo-spherical type ⋮ Fourth order evolution equations which describe pseudospherical surfaces ⋮ A class of quasilinear second order partial differential equations which describe spherical or pseudospherical surfaces ⋮ CBC Systems with Mikhailov Reductions by Coxeter Automorphism: I. Spectral Theory of the Recursion Operators ⋮ Inverse Scattering and the Bäcklund Transformation for the Generalized Wave and Generalized Sine‐Gordon Equations ⋮ Direct and inverse scattering for selfadjoint Hamiltonian systems on the line ⋮ Nonlocal symmetries and the Kaup–Kupershmidt equation

This page was built for publication: Scattering and inverse scattering for first-order systems: II