Numerical Study of Oscillatory Regimes in the Kadomtsev-Petviashvili Equation
Christian Klein, Peter Markowich, and Christof Sparber
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Submission date: 28. Dec. 2005
published in: Journal of nonlinear science, 17 (2007) 5, p. 429-470
DOI number (of the published article): 10.1007/s00332-007-9001-y
MSC-Numbers: 37K10, 35Q53, 34E05, 35Q55
Keywords and phrases: kadomtsev-petviashvili equation, nonlinear dispersive models, multiple scales expansion, modulation theory, davey-stewartson system
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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.