Integration of a Nonlinear Hirota Type Equation with Finite Density in the Class of Periodic Functions

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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