Abstract
Camassa-Holm model is capable of characterizing the dynamic behavior of shallow water wave, thus has been extensively studied. This paper is concerned with shallow water wave behavior after wave breaking. To better reflect the whole process, the modified two-component Camassa-Holm system is considered. The continuation of solutions of such system after wave braking is investigated. By introducing a skillfully defined characteristic, together with a set of newly defined variables, the original system is converted into a Lagrangian equivalent system, from which global dissipative solutions are obtained. The results obtained herein are deemed useful in understanding the dynamic behavior of shallow water wave during and after wave breaking. © 2013 Springer Basel.
| Original language | English |
|---|---|
| Pages (from-to) | 339-360 |
| Number of pages | 22 |
| Journal | Nonlinear Differential Equations and Applications |
| Volume | 21 |
| Issue number | 3 |
| Early online date | 22 Sept 2013 |
| DOIs | |
| Publication status | Published - Jun 2014 |
| Externally published | Yes |
Funding
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). The authors would like to thank the referees for their constructive suggestions and comments.
Keywords
- Dissipative solutions
- Global solutions
- Lagrangian variables
- The modified two-component Camassa-Holm system