Numerical study of oscillatory regimes in the kadomtsev-petviashvili equation

Christian Klein*, Christof Sparber, Peter Markowich

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

48 Scopus citations

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 languageEnglish (US)
Pages (from-to)429-470
Number of pages42
JournalJournal of Nonlinear Science
Volume17
Issue number5
DOIs
StatePublished - Oct 1 2007

Keywords

  • Davey-Stewartson system
  • Kadomtsev-Petviashvili equation
  • Modulation theory
  • Multiple scales expansion
  • Nonlinear dispersive models

ASJC Scopus subject areas

  • Modeling and Simulation
  • Engineering(all)
  • Applied Mathematics

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