Commun. Comput. Phys., 6 (2009), pp. 1022-1062.


Numerical Study of Solutions of the 3D Generalized Kadomtsev-Petviashvili Equations for Long Times

F. Hamidouche 1, Y. Mammeri 2*, S. M. Mefire 3

1 Laboratoire de Mathematiques, CNRS UMR 8628, Universite Paris-Sud 11, 91405 Orsay Cedex, France.
2 Laboratoire de Mathematiques - Paul Painleve, CNRS UMR 8524, Universite des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq Cedex, France.
3 Laboratoire Amienois de Mathematique Fondamentale et Applique, CNRS UMR 6140, Universite de Picardie, 33 r. Saint-Leu, 80039 Amiens Cedex 1, France.

Received 17 July 2008; Accepted (in revised version) 18 December 2008
Available online 8 May 2009

Abstract

From a spectral method combined with a predictor-corrector scheme, we numerically study the behavior in time of solutions of the three-dimensional generalized Kadomtsev-Petviashvili equations. In a systematic way, the dispersion, the blow-up in finite time, the solitonic behavior and the transverse instabilities are numerically inspected.

AMS subject classifications: 35B05, 35B35, 35Q53, 65L05, 65M70

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Key words: 3D-KP equations, spectral method, predictor-corrector method, dispersion, blow-up, soliton, transverse instability.

*Corresponding author.
Email: Youcef.Mammeri@math.univ-lille1.fr (Y. Mammeri), Seraphin.Mefire@u-picardie.fr (S. M. Mefire)
 

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