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A numerical study of the long-wave short-wave resonance for 3D water waves

✍ Scribed by Christophe Besse; David Lannes

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
471 KB
Volume
20
Category
Article
ISSN
0997-7546

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✦ Synopsis

When long-wave short-wave resonance occurs, Davey-Stewartson systems become singular and have to be replaced by another system of equations. This is this system we study here numerically. We use a finite difference scheme for which we prove existence and uniqueness of a solution. We also prove a stability theorem and compute some invariants of the discrete system. We finally give and comment numerical experiments to study the behaviour of the solutions.

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