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Title: Generalized solitary waves in the gravity‐capillary Whitham equation
Abstract

We study the existence of traveling wave solutions to a unidirectional shallow water model, which incorporates the full linear dispersion relation for both gravitational and capillary restoring forces. Using functional analytic techniques, we show that for small surface tension (corresponding to Bond numbers between 0 and 1/3) there exists small amplitude solitary waves that decay to asymptotically small periodic waves at spatial infinity. The size of the oscillations in the far field are shown to be small beyond all algebraic orders in the amplitude of the wave.

 
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PAR ID:
10460571
Author(s) / Creator(s):
 ;  
Publisher / Repository:
Wiley-Blackwell
Date Published:
Journal Name:
Studies in Applied Mathematics
Volume:
144
Issue:
1
ISSN:
0022-2526
Page Range / eLocation ID:
p. 102-130
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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