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Volume 11
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Article

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

by
Vladislav V. Kravchenko
and
Lady Estefania Murcia-Lozano
*
Department of Mathematics, Cinvestav, Campus Querétaro, Libramiento Norponiente #2000, Fracc. Real de Juriquilla, Querétaro 76230, Mexico
*
Author to whom correspondence should be addressed.
Mathematics 2023, 11(16), 3544; https://doi.org/10.3390/math11163544
Submission received: 19 July 2023 / Revised: 6 August 2023 / Accepted: 7 August 2023 / Published: 16 August 2023
(This article belongs to the Special Issue Direct and Inverse Spectral Problems for Ordinary Differential and Functional-Differential Operators)
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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 non-selfadjoint Schrödinger operator; Jost solution; direct scattering problem; inverse scattering problem

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MDPI and ACS Style

Kravchenko, V.V.; Murcia-Lozano, L.E. An Approach to Solving Direct and Inverse Scattering Problems for Non-Selfadjoint Schrödinger Operators on a Half-Line. Mathematics 2023, 11, 3544. https://doi.org/10.3390/math11163544

AMA Style

Kravchenko VV, Murcia-Lozano LE. An Approach to Solving Direct and Inverse Scattering Problems for Non-Selfadjoint Schrödinger Operators on a Half-Line. Mathematics. 2023; 11(16):3544. https://doi.org/10.3390/math11163544

Chicago/Turabian Style

Kravchenko, Vladislav V., and Lady Estefania Murcia-Lozano. 2023. "An Approach to Solving Direct and Inverse Scattering Problems for Non-Selfadjoint Schrödinger Operators on a Half-Line" Mathematics 11, no. 16: 3544. https://doi.org/10.3390/math11163544

APA Style

Kravchenko, V. V., & Murcia-Lozano, L. E. (2023). An Approach to Solving Direct and Inverse Scattering Problems for Non-Selfadjoint Schrödinger Operators on a Half-Line. Mathematics, 11(16), 3544. https://doi.org/10.3390/math11163544

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