Integration of a Nonlinear Hirota Type Equation with Finite Density in the Class of Periodic Functions
А. Б. ХасановSamarkand State University named after Sharof Rashidov, 140104, Samarkand, UzbekistanRaykhonbek Khubaydullo ugli EshbekovSamarkand State University named after Sharof Rashidov, 140104, Samarkand, UzbekistanKh. N. NormurodovSamarkand State University named after Sharof Rashidov, 140104, Samarkand, Uzbekistan
ABI
Abstract
In this paper, the inverse spectral problem method is used to integrate a nonlinear Hirota-type equation with a finite density in the class of periodic functions. The evolution of the spectral data of the periodic Dirac operator is introduced and the coefficient of the Dirac operator is a solution of the nonlinear Hirota equation with a finite density. The solvability of the Cauchy problem for an infinite system of Dubrovin differential equations in the class of sixfold continuously differentiable periodic functions is proven.
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