Inverse scattering problem for operators with a finite dimensional non-local potential
Classical Analysis and ODEs
2023-12-25 v1 Mathematical Physics
math.MP
Abstract
Scattering problem for a self-adjoint integro-differential operator, which is the sum of the operator of second derivative and of a finite-dimensional self-adjoint operator, is studied. Jost solutions are found and it is shown that the scattering function has a multiplicative structure, besides, each of the multipliers is a scattering coefficient for a pair of self-adjoint operators, one of which is a one-dimensional perturbation of the other. Solution of the inverse problem is based upon the solutions to the inverse problem for every multiplier. A technique for finding parameters of the finite-dimensional perturbation via the scattering data is described.
Cite
@article{arxiv.2312.14545,
title = {Inverse scattering problem for operators with a finite dimensional non-local potential},
author = {Vladimir A. Zolotarev},
journal= {arXiv preprint arXiv:2312.14545},
year = {2023}
}