Resolvent approach for two-dimensional scattering problems. Application to the nonstationary Schrödinger problem and the KPI equation

M. Boiti, F. Pempinelli, A. K. Pogrebkov, M. C. Polivanov

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)

Abstract

The resolvent operator of the linear problem is determined as the full Green function continued in the complex domain in two variables. An analog of the known Hilbert identity is derived. We demonstrate the role of this identity in the study of two-dimensional scattering. Considering the nonstationary Schrödinger equation as an example, we show that all types of solutions of the linear problems, as well as spectral data known in the literature, are given as specific values of this unique function - the resolvent function. A new form of the inverse problem is formulated.

Original languageEnglish
Pages (from-to)1200-1224
Number of pages25
JournalTheoretical and Mathematical Physics
Volume93
Issue number2
DOIs
Publication statusPublished - Nov 1992
Externally publishedYes

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