Search

MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS Preprint
124/2005

Numerical Study of Oscillatory Regimes in the Kadomtsev-Petviashvili Equation

Christian Klein, Peter Markowich and Christof Sparber

Abstract

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:
Dec 28, 2005
Published:
Dec 28, 2005
MSC Codes:
37K10, 35Q53, 34E05, 35Q55
Keywords:
kadomtsev-petviashvili equation, nonlinear dispersive models, multiple scales expansion, modulation theory, davey-stewartson system

Related publications

inJournal
2007 Repository Open Access
Christian Klein, Christof Sparber and Peter Markowich

Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili Equation

In: Journal of nonlinear science, 17 (2007) 5, pp. 429-470