Abstract
This paper investigates the dynamic behavior of the modified coupled two-component Camassa-Holm dynamic system arisen from shallow water waves moving. By using a skillfully defined characteristic and a set of newly introduced variables, the original system is converted into a Lagrangian semilinear one in which the associated energy is introduced as an additional variable so as to obtain a well-posed initial-value problem, facilitating the study on the behavior of wave breaking. It is established that the solutions of the system continue as global dissipative solutions after wave breaking, which presents an interesting and useful result for better understanding the inevitable phenomenon before and after wave breaking. © 2013 Springer-Verlag Berlin Heidelberg.
| Original language | English |
|---|---|
| Pages (from-to) | 2007-2019 |
| Number of pages | 13 |
| Journal | Soft Computing |
| Volume | 17 |
| Issue number | 11 |
| Early online date | 11 Sept 2013 |
| DOIs | |
| Publication status | Published - Nov 2013 |
| Externally published | Yes |
Funding
The authors would like to thank the referees for their constructive suggestions and comments. The paper is supported by the Major State Basic Research Development Program 973 (No. 2012CB215202), the National Natural Science Foundation of China (No. 60974052 and 61134001) and the Fundamental Research Funds for the Central Universities (No. CDJXS12170003).
Keywords
- Dissipative solutions
- Global solutions
- The modified coupled two-component Camassa-Holm system