Integration of the loaded MKDV equation with a source in the class of rapidly decreasing functions

We consider the Cauchy problem for a loaded modi ed Korteweg-de Vries equation with a self-consistent source. The evolution of the scattering data of the Dirac operator, whose potential is a solution of the loaded modi ed Korteweg-de Vries equation with a self-consistent source in the class of rapidly decreasing functions, is derived. A specific example is given to illustrate the application of the obtained results.