An Isaac Newton Institute Workshop

The Theory of Highly Oscillatory Problems

Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation

Authors: Christian Klein (Max Planck Institute for Mathematics in the Sciences), Christof Sparber (Wolfgang Pauli Institute Vienna & Faculty of Mathematics, Vienna University), Peter Markowich (Faculty of Mathematics, Vienna University)

Abstract

The aim of this talk 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 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.

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