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March 2005 Three-dimensional Localized Solitary Gravity-Capillary Waves
Paul A. Milewski
Commun. Math. Sci. 3(1): 89-99 (March 2005).


In a weakly nonlinear model equation for capillary-gravity water waves on a two-dimensional free surface, we show, numerically, that there exist localized solitary traveling waves for a range of parameters spanning from the long wave limit (with Bond number B>1/3, in the regime of the Kadomtsev-Petviashvilli-I equation) to the wavepacket limit (B>1/3, in the Davey-Stewartson regime). In fact, we show that these two regimes are connected with a single continuous solution branch of nonlinear localized solitary solutions crossing B=1/3.


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Paul A. Milewski. "Three-dimensional Localized Solitary Gravity-Capillary Waves." Commun. Math. Sci. 3 (1) 89 - 99, March 2005.


Published: March 2005
First available in Project Euclid: 17 March 2005

zbMATH: 1073.76009
MathSciNet: MR2132827

Rights: Copyright © 2005 International Press of Boston

Vol.3 • No. 1 • March 2005
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