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

A. B. Khasanov^a, G. U. Urazboev

^a Faculty of Physics and Mathematics, Urgench State University

Abstract: 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.

Key words: method of the inverse scattering problem, nonlinear evolutionary equation, the sine-Gordon equation, scattering data.

UDC: 517.946

Received: 22.02.2007

 English version: Siberian Advances in Mathematics, 2009, 19:1, 13–23

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