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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
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
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
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https://www.mathnet.ru/eng/ivm9964 https://www.mathnet.ru/eng/ivm/y2024/i3/p70
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Abstract page: | 54 | Full-text PDF : | 2 | References: | 17 | First page: | 5 |
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