Integrating the modified Korteweg–de Vries– sine-Gordon equation in the class of periodic infinite-gap functions
А. Б. ХасановSamarkand State University, Samarkand, UzbekistanKh. N. NormurodovSamarkand State University, Samarkand, UzbekistanU. O. KhudaerovSamarkand Architectural and Construction Institute, Samarkand, Uzbekistan
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Annotatsiya
The inverse spectral problem method is used to integrate the nonlinear modified Korteweg–de Vries–sine-Gordon equation 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 six-times continuously differentiable periodic infinite-gap functions is proved. It is shown that the sum of a uniformly converging functional series constructed with the use of a solution of a system of Dubrovin equations and the first trace formula satisfies the modified Korteweg–de Vries–sine-Gordon equation.
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