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Abstract and Applied Analysis
Volume 2013, Article ID 437473, 12 pages
http://dx.doi.org/10.1155/2013/437473
Research Article

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

School of Automation, Chongqing University, Chongqing 400044, China

Received 11 August 2013; Accepted 24 October 2013

Academic Editor: Sining Zheng

Copyright © 2013 Yujuan Wang and Yongduan Song. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.