The Cauchy Problem for the Nonlinear Complex Modified Korteweg-de Vries Equation with Additional Terms in the Class of Periodic Infinite-Gap Functions

We use the inverse spectral problem method for integrating the nonlinear complexmodified Korteweg-de Vries equation (cmKdV) with additional terms in the classof periodic infinite-gap functions. Also, we deduce the evolution of the spectral dataof the periodic Dirac operator whose coefficient is a solution to cmKdV.We prove that the Cauchy problem is solvable for an infinite system of Dubrovindifferential equations in the class of six times continuously differentiableperiodic infinite-gap functions. Moreover, we establish the solvabilityof the Cauchy problem for cmKdV with additional terms in the class of sixtimes continuously differentiable periodic infinite-gap functions.