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Inverse scattering for the non-linear Schrödinger equation: Reconstruction of the potential and the non-linearity

✍ Scribed by Ricardo Weder

Publisher
John Wiley and Sons
Year
2001
Tongue
English
Weight
106 KB
Volume
24
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

In this paper we consider the inverse scattering problem for the non‐linear Schrödinger equation on the line

\def\dr{{\rm d}}$$i{\partial\over\partial t}u(t,x)=‐{\dr^2\over\dr x^2}u(t,x)+V_0(x)u(t,x)+\sum_{j=1}^{\infty}V_j(x)|u|^{2(j_0+j)}u(t,x)$$\nopagenumbers\end

We prove, under appropriate conditions, that the small‐amplitude limit of the scattering operator determines uniquely V~j~, j=0,1,… . Our proof gives also a method for the reconstruction of the V~j~, j=0,1,… . Copyright © 2001 John Wiley & Sons, Ltd.

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