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Consistency of the KP approximation

Pages: 517 - 525, Issue Special, July 2003

 Abstract        Full Text (194.6K)              

D. Lannes - MAB, Université Bordeaux I and CNRS UMR 5466, 351 Cours de la Libération, 33405 Talence Cedex, France (email)

Abstract: We consider here the consistency of the KP approximation for a Boussinesq system. We consider the general case of two counterpropagating waves, which do not have to satisfy strong zero mass assumptions. We show that without such strong assumption, the KP approximation is not consistent with the Boussinesq system, but that it is close to a consistent approximation. We give precise consistency results, and also consider the case were no zero mass assumption at all is made.

Keywords:  water-waves, Kadomtsev-Petviashvili equations, consistency.
Mathematics Subject Classification:  35B40, 35Q35, 35Q53.

Received: September 2002;      Revised: April 2003;      Published: April 2003.