Integration of the Loaded Sine-Gordon Equation by the Inverse Scattering Problem Method
Urazboev G.U. Baltaeva I.I. Baimankulov A.T.
2024Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan
Azerbaijan Journal of Mathematics
2024#14Issue 144 - 55 pp.
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.
Cauchy-Goursat problem , Dirac operator , evolution of scattering data , inverse scattering method , loaded sine-Gordon equation
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Urgench state university and Institute of mathematics named after V.I.Romanovsky, Urgench, 220100, Uzbekistan
Urgench state university, Urgench, 220100, Uzbekistan
A.Baitursynov Kostanay Regional University, Tauelsizdik Street 118, Kostanai, Kazakhstan
Urgench state university and Institute of mathematics named after V.I.Romanovsky
Urgench state university
A.Baitursynov Kostanay Regional University
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