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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2024, Number 3, Pages 70–83
DOI: https://doi.org/10.26907/0021-3446-2024-3-70-83
(Mi ivm9964)
 

Integration of a sine-Gordon type equation with an additional term in the class of periodic infinite-gap functions

A. B. Khasanov, Kh. N. Normurodov

Samarkand State University, 15 University blvd. str., Samarkand, 140104 Republic of Uzbekistan
References:
Abstract: In this paper, the inverse spectral problem method is used to integrate a nonlinear sine-Gordon type equation with an additional term in the class of periodic infinite-gap functions. The solvability of the Cauchy problem for an infinite system of Dubrovin differential equations in the class of three times continuously differentiable periodic infinite-gap functions is proved. It is shown that the sum of a uniformly convergent functional series constructed by solving the system of Dubrovin equations and the first trace formula satisfies sine-Gordon-type equations with an additional term.
Keywords: sine-Gordon type equation, Dirac operator, spectral data, Dubrovin's system of equations, trace formula.
Received: 27.01.2023
Revised: 07.10.2023
Accepted: 26.12.2023
Document Type: Article
UDC: 517.957
Language: Russian
Citation: A. B. Khasanov, Kh. N. Normurodov, “Integration of a sine-Gordon type equation with an additional term in the class of periodic infinite-gap functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, no. 3, 70–83
Citation in format AMSBIB
\Bibitem{KhaNor24}
\by A.~B.~Khasanov, Kh.~N.~Normurodov
\paper Integration of a sine-Gordon type equation with an additional term in the class of periodic infinite-gap functions
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2024
\issue 3
\pages 70--83
\mathnet{http://mi.mathnet.ru/ivm9964}
\crossref{https://doi.org/10.26907/0021-3446-2024-3-70-83}
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