Inverse scattering problem for a third-order operator with non-local potential

TL;DR

This paper addresses the inverse scattering problem for a third-order operator with a non-local potential, employing a Riemann boundary value problem approach on a bundle of three lines to characterize scattering data.

Contribution

It introduces a novel method based on Riemann boundary value problems for solving inverse scattering for third-order operators with non-local potentials.

Findings

Solved direct and inverse scattering problems for the operator.

Provided a description of scattering data.

Developed a new analytical approach using Riemann boundary value problems.

Abstract

Direct and inverse scattering problem for an operator with non-local potential is solved in the paper. The method is based on the Riemann boundary value problem on a bundle of three straight lines. Description of scattering problem data is given.