Existence and Uniqueness of Time Periodic Solution to the Viscous Modified Degasperis-Procesi Equation

In this paper, we establish the existence and uniqueness criteria of time periodic solution to the viscous modified Degasperis-Procesi (vmDP for short) equation with periodic boundary value conditions. The analysis of this study is based on Galerkin’s method and Leray-Schauder fixed point theorem. Using Galerkin’s method some uniform priori estimates of approximate solution to the corresponding equation of vmDP has been constructed. Furthermore, the efficient and straightforward existence and uniqueness criteria of time periodic solution to the vmDP with periodic boundary value conditions has been obtained.