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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Vladislav V. Kravchenko & Lady Estefania Murcia-Lozano, 2023. "An Approach to Solving Direct and Inverse Scattering Problems for Non-Selfadjoint Schrödinger Operators on a Half-Line," Mathematics, MDPI, vol. 11(16), pages 1-51, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3544-:d:1218603
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