A discrete version of the two-dimensional inverse scattering problem is
considered. On this basis, algebraic transformations for the two-dimensional
finite-difference Schredinger equation are elaborated.Comment: 12 pages, 1 figure (s_fig.eps), Late

Suzko, A. A.

English

arXiv

A discrete version of the two-dimensional inverse scattering problem is considered. On this basis, algebraic transformations for the two-dimensional finite-difference Schrödinger equation are elaborated. Generalization of the technique of one-dimensional Darboux transformations for the two-dimensional finite-difference Schrödinger equation is presented. Ideas of Bargmann-Darboux transformations for the differential one-dimensional multichannel Schrödinger equation are used for the two-dimensional lattice Schrödinger equation. Analytic relationships are established between different discrete potentials and the corresponding solutions

A. A. Suzko

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Inverse problem and Darboux transformations for two-dimensional finite-difference Schrödinger equation

http://www.mat.univie.ac.at/~esiprpr/esi665.pdf

Inverse problem and Darboux transformations for two-dimensional finite-difference Schredinger equation

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