Geodesic
Integrating the~modified Korteweg--de~Vries--\allowbreak sine-Gordon equation in the~class of periodic infinite-gap functions
Teoretičeskaâ i matematičeskaâ fizika, Tome 214 (2023) no. 2, pp. 198-210

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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.
Keywords: modified Korteweg–de Vries–sine-Gordon equation, Dirac operator, spectral data, system of Dubrovin equations, trace formulas. 
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     author = {A. B. Khasanov and Kh. N. Normurodov and U. O. Hudayerov},
     title = {Integrating the~modified {Korteweg--de~Vries--\allowbreak} {sine-Gordon} equation in the~class of periodic infinite-gap functions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2023_214_2_a1/}
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A. B. Khasanov; Kh. N. Normurodov; U. O. Hudayerov. Integrating the~modified Korteweg--de~Vries--\allowbreak sine-Gordon equation in the~class of periodic infinite-gap functions. Teoretičeskaâ i matematičeskaâ fizika, Tome 214 (2023) no. 2, pp. 198-210. http://geodesic.mathdoc.fr/item/TMF_2023_214_2_a1/