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Reconstruction of the Schrödinger-equation potential from scattering data by the Krein method

✍ Scribed by I. V. Poplavskii

Book ID
112416200
Publisher
Springer
Year
1968
Tongue
English
Weight
222 KB
Volume
11
Category
Article
ISSN
1573-9228

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Inverse scattering for the non-linear Schrödinger equation: Reconstruction of the potential and the non-linearity
✍ Ricardo Weder 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 106 KB

## 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, unde