Periodic Conservative Solutions for a Modified Two-Component Camassa-Holm System with Peakons

Abstract

This paper investigates the periodically weak conservative solutions for a modified periodic two-component Camassa-Holm system arisen from shallow water waves moving. The underlying approach is based on a system reformulation by introducing a skillfully defined characteristic and a set of newly defined variables. Such treatment makes it possible to overcome the difficulties inherent in the multicomponent system, leading to the establishment of the periodic conservative solutions for the original system.