On the generalized nonlinear Camassa–Holm equation

Abstract

In this paper, a generalized nonlinear Camassa–Holm equation with time- and space-dependent coefficients is considered. We show that the control of the higher order dispersive term is possible by using an adequate weight function to define the energy. The existence and uniqueness of solutions are obtained via a standard Picard iterative method, so that there is no loss of regularity of the solution with respect to the initial condition in some appropriate Sobolev space.