Multidimensional Analogues of Gelfand–Levitan, Marchenko and Krein Equations. Theory, Numerics and Applications

Authors

  • Sergey Kabanikhin 1Institute of Computational Mathematics and Mathematical Geophysics
  • Maxim Shishlenin 1Institute of Computational Mathematics and Mathematical Geophysics

Keywords:

Gelfand-Levitan equation, Krein equation, Marchenko equation, inverse coefficient problem, inverse scattering problem

Abstract

We consider the method of regularization of two dimensional (2D) inverse coefficient
problems based on the projection method and the approach of I.M. Gelfand, B.M. Levitan, M.G.
Krein and V.A. Marchenko. We propose a method of reconstruction of the potential, density and
velocity in 2D inverse coefficient problems. The 2D analogies of the I.M. Gelfand, B.M. Levitan and
M.G. Krein method are established. The 2D analog of the V.A. Marchenko equation is considered
for the Kadomtsev-Petviashvili equation. This approach can be easily applied to corresponding
multidimensional inverse problems. The results of numerical calculations are presented.

Downloads

Published

2018-09-28

Issue

Vol. 86 No. 3 (2015): Journal of Mathematics, Mechanics and Computer Science

Section

Mathematical modeling of technological processes

How to Cite

Multidimensional Analogues of Gelfand–Levitan, Marchenko and Krein Equations. Theory, Numerics and Applications. (2018). Journal of Mathematics, Mechanics and Computer Science, 86(3), 63-69. https://bm.kaznu.kz/index.php/kaznu/article/view/498