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On the sine-Gordon equation with a self-consistent source

А. Б. ХасановDepartment of Mathematics, Urgench State University, Urgench, 220110, UzbekistanG. U. UrazboevDepartment of Mathematics, Urgench State University, Urgench, 220110, Uzbekistan
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We use the method of the inverse scattering problem to solve the sine-Gordon equation with a self-consistent source which corresponds to moving eigenvalues of the corresponding spectral problem.

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