MiS Preprint Repository
We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Numerical Study of Oscillatory Regimes in the Kadomtsev-Petviashvili Equation
Christian Klein, Peter Markowich and Christof SparberAbstract
The aim of this paper is the accurate numerical study of the 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 a Davey-Stewartson type 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.
- Received:
- 28.12.05
- Published:
- 28.12.05
- MSC Codes:
- 37K10, 35Q53, 34E05, 35Q55
- Keywords:
- kadomtsev-petviashvili equation, nonlinear dispersive models, multiple scales expansion, modulation theory, davey-stewartson system