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
ABI
Аннотация
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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