Solitary gravity-capillary water waves with point vortices

Kristoffer  Varholm

doi:10.3934/dcds.2016.36.3927

Article Contents

2016, Volume 36, Issue 7: 3927-3959. Doi: 10.3934/dcds.2016.36.3927

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Solitary gravity-capillary water waves with point vortices

Kristoffer Varholm^1,

1.
Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim

Received: April 30, 2015

Revised: October 31, 2015

Published: May 2017

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Abstract

We construct small-amplitude solitary traveling gravity-capillary water waves with a finite number of point vortices along a vertical line, on finite depth. This is done using a local bifurcation argument. The properties of the resulting waves are also examined: We find that they depend significantly on the position of the point vortices in the water column.

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Mathematics Subject Classification: Primary: 35Q31; Secondary: 35C07, 76B25.

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