An Approach to Solving Direct and Inverse Scattering Problems for Non-Selfadjoint Schrödinger Operators on a Half-Line

Vladislav V. Kravchenko and Lady Estefania Murcia-Lozano ()
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Vladislav V. Kravchenko: Department of Mathematics, Cinvestav, Campus Querétaro, Libramiento Norponiente #2000, Fracc. Real de Juriquilla, Querétaro 76230, Mexico
Lady Estefania Murcia-Lozano: Department of Mathematics, Cinvestav, Campus Querétaro, Libramiento Norponiente #2000, Fracc. Real de Juriquilla, Querétaro 76230, Mexico

Mathematics, 2023, vol. 11, issue 16, 1-51

Abstract: In this paper, an approach to solving direct and inverse scattering problems on the half-line for a one-dimensional Schrödinger equation with a complex-valued potential that is exponentially decreasing at infinity is developed. It is based on a power series representation of the Jost solution in a unit disk of a complex variable related to the spectral parameter by a Möbius transformation. This representation leads to an efficient method of solving the corresponding direct scattering problem for a given potential, while the solution to the inverse problem is reduced to the computation of the first coefficient of the power series from a system of linear algebraic equations. The approach to solving these direct and inverse scattering problems is illustrated by several explicit examples and numerical testing.

Keywords: non-selfadjoint Schrödinger operator; Jost solution; direct scattering problem; inverse scattering problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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