Integration of a Nonlinear Complex Modified Korteweg–De Vries Equation with Additional Terms

Annotatsiya

In this paper, the inverse spectral problem method is used to integrate a complex modified Korteweg-de Vries(cmKdV) equation with additional terms in the class of periodic infinite-gap functions. The evolution of the spectral data of the periodic Dirac operator is introduced, and the coefficient of the Dirac operator is a solution to cmKdV equation with additional terms. A simple algorithm for deriving the Dubrovin system of differential equations is proposed. The solvability of the Cauchy problem for a Dubrovin infinite system of differential equations in the class of six times continuously differentiable periodic infinite-gap functions is proven.