Integration of the Loaded Sine-Gordon Equation by the Inverse Scattering Problem Method

Gayrat Urazaliyevich Urazboev, Iroda Ismailovna Baltaeva, A. T. Baimankulov

2024

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DOI 10.59849/2218-6816.2024.1.44
Data confidence 70 medium
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Abstract

In this paper, we consider the Cauchy-Goursat problem for a loaded sine-Gordon equation.The main results of the work are the theorem on the uniqueness of the solution of the problem under consideration and the theorem on the evolution of the scattering data of the Dirac operator whose potential is related to the solution of the loaded sine-Gordon equation.The equalities obtained in the scattering data evolution theorem make it possible to apply the method of inverse scattering problem to solve the considered problem.