Abstract
The aim of this paper is the accurate numerical study of the Kadomtsev-Petviashvili (KP) equation. In particular, we are concerned with the small dispersion limit of this model, where no comprehensive analytical description exists so far. To this end, we first study a similar highly oscillatory regime for asymptotically small solutions, which can be described via the Davey-Stewartson system. In a second step, we investigate numerically the small dispersion limit of the KP model in the case of large amplitudes. Similarities and differences to the much better studied Korteweg-de Vries situation are discussed as well as the dependence of the limit on the additional transverse coordinate.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 429-470 |
| Number of pages | 42 |
| Journal | Journal of Nonlinear Science |
| Volume | 17 |
| Issue number | 5 |
| DOIs | |
| State | Published - Oct 2007 |
| Externally published | Yes |
Bibliographical note
Funding Information:Acknowledgements We thank B. Dubrovin, E. Ferapontov, J. Frauendiener, and T. Grava for helpful discussions and hints. This work has been supported by the Wittgenstein Award 2000 of the third author. C.S. has been supported by the APART research grant funded by the Austrian Academy of Sciences. C.K. thanks for financial support by the MISGAM program of the European Science Foundation.
Keywords
- Davey-Stewartson system
- Kadomtsev-Petviashvili equation
- Modulation theory
- Multiple scales expansion
- Nonlinear dispersive models
ASJC Scopus subject areas
- Modeling and Simulation
- General Engineering
- Applied Mathematics