The initial value problem for the Hirota equation with finite density and self-consistent series source

In this paper, we consider the problem of integration of the Hirota equation with finite density and self-consistent series source using the inverse spectral problem method for the periodic Dirac operator in the class of periodic infinite-gap functions. In addition, we derive the evolution of spectral data of the periodic Dirac operator and prove that the solution of the initial value problem for the infinite Dubrovin system of differential equations has a unique solution.