Abstract
Investigated here are interesting aspects of the solitary-wave solutions of the generalized Regularized Long-Wave equation ut + ux + α(up)x - βuxxt = 0. For p > 5, the equation has both stable and unstable solitary-wave solutions, according to the theory of Souganidis and Strauss. Using a high-order accurate numerical scheme for the approximation of solutions of the equation, the dynamics of suitably perturbed solitary waves are examined. Among other conclusions, we find that unstable solitary waves may evolve into several, stable solitary waves and that positive initial data need not feature solitary waves at all in its long-time asymptotics.
| Original language | English |
|---|---|
| Pages (from-to) | 603-638 |
| Number of pages | 36 |
| Journal | Journal of Nonlinear Science |
| Volume | 10 |
| Issue number | 6 |
| DOIs | |
| State | Published - 2000 |
| Externally published | Yes |
Funding
⁄ JMR was supported by an appointment to the Distinguished Postdoctoral Research Program sponsored by the U.S. Department of Energy, Office of University and Science Programs, and administered by the Oak Ridge Institute for Science and Education. The work of WRM was performed at Argonne National Laboratory as a Faculty Research Participant. JLB was partially supported by the National Science Foundation and the W. M. Keck Foundation. The authors thank B. Lucier for supplying a computer code, parts of which were adapted to produce the solver used in this study. We also thank Michael Weinstein for his helpful comments on this study.
Keywords
- BBM equation
- Generalized BBM equation
- Generalized RLW equation
- RLW equation
- Stable solitary-waves
- Unstable solitary-waves