Scattering Data of a Nonlinear Partial Differential Equation with a Lax Pair with a Dirac Scattering Operator of the First Kind

Abstract

This article is devoted to the development of the inverse scattering problem method in relation to a nonlinear partial differential equation with a Lax pair. The Dirac operator of the first kind is used as a scattering operator. The purpose of the article is to solve a direct problem and construct scattering data. In the course of the research, the construction of a fundamental solution system for the Dirac operator with given conditions and a transition matrix from one solution basis to another are considered step by step. In the process of studying the problem, a detailed analysis of the dynamics of the elements of the scattering matrix was carried out, and the case of discrete eigenvalues of the Dirac operator was considered.