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

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2024), pp. 70-83

Résumé

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.

Détail

Mots-clés : sine-Gordon type equation, trace formula.
Keywords: Dirac operator, spectral data, Dubrovin's system of equations

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