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June  2010, 13(4): 859-872. doi: 10.3934/dcdsb.2010.13.859

On the transverse instability of one dimensional capillary-gravity waves

Frédéric Rousset 1, and  Nikolay Tzvetkov 2,

1. 

IRMAR, Université de Rennes 1, campus de Beaulieu, 35042 Rennes cedex, France
2. 

Département de Mathématiques, Université Lille I, 59 655 Villeneuve d’Ascq Cedex, France

Received  March 2009 Revised  July 2009 Published  March 2010

This text represents the content of a talk given by the second author at ENS Paris on January 28, 2009 at the conference "Mathematics and Oceanography". We are grateful to David Gérard-Varet, David Lannes and Laure Saint-Raymond for the kind invitation to present our recent work on the water waves. The proofs of the results announced here will appear in [18].
Keywords: water-waves., free boundary problems, solitary waves, stability.
Mathematics Subject Classification: 35B35, 35B45, 35C08, 35Q31, 35R3.
Citation: Frédéric Rousset, Nikolay Tzvetkov. On the transverse instability of one dimensional capillary-gravity waves. Discrete & Continuous Dynamical Systems - B, 2010, 13 (4) : 859-872. doi: 10.3934/dcdsb.2010.13.859
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