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.