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A plethora of generalised solitary gravity–capillary water waves

Published online by Cambridge University Press:  06 November 2015

Didier Clamond*
Affiliation:
Université de Nice – Sophia Antipolis, Laboratoire J. A. Dieudonné, Parc Valrose, 06108 Nice CEDEX 2, France
Denys Dutykh
Affiliation:
Université Savoie Mont Blanc, LAMA, UMR 5127 CNRS, Campus Scientifique, 73376 Le Bourget-du-Lac CEDEX, France
Angel Durán
Affiliation:
Departamento de Matemática Aplicada, E.T.S.I. Telecomunicación, Campus Miguel Delibes, Universidad de Valladolid, Paseo de Belen 15, 47011 Valladolid, Spain
*
Email address for correspondence: didierc@unice.fr

Abstract

The present study describes, first, an efficient algorithm for computing solutions in terms of capillary–gravity solitary waves of the irrotational Euler equations with a free surface and, second, provides numerical evidences of the existence of an infinite number of generalised solitary waves (solitary waves with undamped oscillatory wings). Using conformal mapping, the unknown fluid domain, which is to be determined, is mapped into a uniform strip of the complex plane. In the transformed domain, a Babenko-like equation is then derived and solved numerically.

Type
Papers
Copyright
© 2015 Cambridge University Press 

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