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Mathematical Problems in Engineering
Volume 2013, Article ID 107450, 11 pages
http://dx.doi.org/10.1155/2013/107450
Research Article

On the Multipeakon Dissipative Behavior of the Modified Coupled Camassa-Holm Model for Shallow Water System

1School of Automation, Chongqing University, Chongqing 400044, China
2Department of Engineering, Faculty of Technology and Science, University of Agder, N-4898 Grimstad, Norway

Received 9 May 2013; Accepted 26 June 2013

Academic Editor: Hongli Dong

Copyright © 2013 Zhixi Shen et al. 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 multipeakon dissipative behavior of the modified coupled two-component Camassa-Holm system arisen from shallow water waves moving. To tackle this problem, we convert the original partial differential equations into a set of new differential equations by using skillfully defined characteristic and variables. Such treatment allows for the construction of the multipeakon solutions for the system. The peakon-antipeakon collisions as well as the dissipative behavior (energy loss) after wave breaking are closely examined. The results obtained herein are deemed valuable for understanding the inherent dynamic behavior of shallow water wave breaking.