THE CAUCHY PROBLEM FOR THE MODIFIED KORTEWEG-DE VRIES-LIOUVILLE (MKDV-L) EQUATION WITH AN ADDITIONAL TERM IN THE CLASS OF PERIODIC INFINITE-GAP FUNCTIONS.

In this paper, the inverse spectral problem method is used to integrate a modified Korteweg-de Vries-Liouville (mKdV-L) equation with an additional term 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 for a modified Korteweg-de Vries-Liouville equation with an additional term. 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. It is proven that there is a global solution of the Cauchy problem for a modified Korteweg-de Vries-Liouville equation with an additional term for sufficiently smooth initial conditions. [ABSTRACT FROM AUTHOR]