ABOUT THE CAMASSA-HOLM EQUATION WITH A SELF-CONSISTENT SOURCE

The paper is devoted to solving the Camassa-Holm equation with a self-consistent source of a special type by the inverse scattering method. The main result consists in determining the evolution of the scattering data for the spectral problem associated with the Camassa-Holm equation with a self-consistent source of a special type. In contrast to the classical Camassa-Holm equation, the eigenvalues of the spectral problem are moving in the problem under consideration. The resulting equalities determine the evolution of the scattering data completely; this fact allows us to apply the inverse scattering method for solving the considered problem.