Integration of the Negative-Order ModifiedKorteweg–de Vries Equation with a Loaded Termin the Class of Periodic Functions

Spectral data of the Dirac operator with periodic potential are found. This operator is associated with the negative-order modified Korteweg–de Vries equation with a loaded term. The results obtained permit one to construct a solution of the negative-order modified Korteweg–de Vries equation with a loaded term in the class of periodic functions using the inverse spectral problem method. The solvability of the Cauchy problem for an infinite system of Dubrovin–Trubowitz differential equations in the class of three times continuously differentiable periodic functions is proved.