Decay and regularity in the inverse scattering problem

DOI10.1016/0022-247X(82)90132-9zbMath0518.35067MaRDI QIDQ1053891

Amy Cohen Murray

Publication date: 1982

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

potentialregularitydecayKorteweg-de Vries equationinverse scattering

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) Schrödinger operator, Schrödinger equation (35J10) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items

Solutions of the Korteweg-de Vries equation with steplike initial data ⋮ Commutation Methods Applied to the mKdV-Equation ⋮ Convergence of a finite difference method for the KdV and modified KdV equations with \(L^2\) data ⋮ On the forced nonlinear Schrödinger equation ⋮ A counterexample in the inverse scattering theory for steplike potentials ⋮ Classical solutions of the korteweg—devries equation for non—smooth initial data via inverse scattering^*

Cites Work

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• Existence and regularity for solutions of the Korteweg-de Vries equation
• Solutions of the Korteweg-de Vries equation from irregular data
• Korteweg-de Vries equation: Construction of solutions in terms of scattering data
• Inverse scattering on the line
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Method for Solving the Korteweg-deVries Equation
• Properties of the 𝑆-matrix of the one-dimensional Schrödinger equation