Inverse scattering and evolution equations

DOI10.1002/cpa.3160380103zbMath0578.35040OpenAlexW2056101558MaRDI QIDQ3700140

Publication date: 1985

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/cpa.3160380103

zbMATH Keywords

existence asymptotic expansion nonlinear Schrödinger equation evolution equations global existence spectral problems operator sine-Gordon equation modified KdV equation solvable scattering data Cauchy-Riemann well-posed evolution Schwartz class solutions generic Schwartz class initial data Schwartz class potential three-wave interaction equation

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) Partial differential equations of mathematical physics and other areas of application (35Q99) Initial value problems for linear higher-order PDEs (35G10) Higher-order parabolic equations (35K25)

Related Items (40)

Inverse scattering on the half-line for ZS-AKNS systems with integrable potentials ⋮ On Darboux transformations for soliton equations in high-dimensional spacetime ⋮ Inverse scattering transform for the vector nonlinear Schrödinger equation with nonvanishing boundary conditions ⋮ Long-time asymptotics for the pure radiation solution of the sine—gordon equation ⋮ The D-bar approach to inverse scattering and nonlinear evolutions ⋮ Letters in Mathematical Physics cumulative index, Volumes 30-32 (1994) ⋮ Linear integral transformations and hierarchies of integrable nonlinear evolution equations ⋮ Gauge theory of Bäcklund transformations. II ⋮ Poisson commuting energies for a system of infinitely many bosons ⋮ On Equations Which Describe Pseudospherical Surfaces ⋮ Integrable many-body problems and functional equations ⋮ Perturbation theory for nearly integrable multicomponent nonlinear PDEs ⋮ Semigroup estimates and stability/instability results for the linearized three waves interaction equations ⋮ Solvability of the derivative nonlinear Schrödinger equation and the massive Thirring model ⋮ On the Dissipative Evolution Equations Associated with the Zakharov-Shabat System with a Quadratic Spectral Parameter ⋮ On equations of type u x t=F(u,u x) which describe pseudospherical surfaces ⋮ On the Caudrey-Beals-Coifman System and the Gauge Group Action ⋮ Completeness of the eigenfunctions for the Caudrey–Beals–Coifman system ⋮ Nonlinear evolution equations related to Kac-Moody algebras $A_r^{(1)}$: spectral aspects ⋮ Three-Wave Interaction Equations: Classical and Nonlocal ⋮ Direct nonlinear Fourier transform algorithms for the computation of solitonic spectra in focusing nonlinear Schrödinger equation ⋮ Strong regularizing effect of integrable systems ⋮ Some features of the maps from potential to spectral data ⋮ Recursion operators and hierarchies of mKdV equations related to the Kac-Moody algebras $D_4^{(1)}$, $D_4^{(2)}$, and $D_4^{(3)}$ ⋮ The symmetries of solitons ⋮ Inverse scattering problems for the Landau-Lifschitz equations ⋮ On the integrability of linear and nonlinear partial differential equations ⋮ On mKdV equations related to Kac-Moody algebras $A_5^{(1)}$ and $A_5^{(2)}$ ⋮ Semiclassical soliton ensembles for the three-wave resonant interaction equations ⋮ Hamiltonian structure for degenerate AKNS systems ⋮ Complete integrability of shock clustering and Burgers turbulence ⋮ The DBAR Problem and the Thirring Model ⋮ The Cauchy problem of the Ward equation ⋮ The mKdV-type equations related to $A_5^{(1)}$ and $A_5^{(2)}$ Kac-Moody algebras ⋮ The Cauchy problem of the Ward equation with mixed scattering data ⋮ Inverse Scattering Transform for the Multi-Component Nonlinear Schrödinger Equation with Nonzero Boundary Conditions ⋮ 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 ⋮ The generalised Zakharov–Shabat system and the gauge group action ⋮ On the complete integrability of completely integrable systems

Cites Work

This page was built for publication: Inverse scattering and evolution equations