The bifurcation of interfacial capillary-gravity waves underO(2) symmetry

Mark Jones

doi:10.3934/cpaa.2011.10.1183

Article Contents

2011, Volume 10, Issue 4: 1183-1204. Doi: 10.3934/cpaa.2011.10.1183

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The bifurcation of interfacial capillary-gravity waves under O(2) symmetry

Mark Jones^1,

1.
School of Mathematics, Kingston University, Kingston-on-Thames, KT1 2EE01103

Received: March 2010

Revised: November 2010

Published: July 2011

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Abstract

The evolution of an interface between two fluids of different densities is considered. The particular case under examination is when the motion is due to an interaction between the Mth and Nth harmonics of the fundamental mode. By means of a hodograph transformation the problem is cast as an operator equation between two suitable function spaces. Classical techniques are used to reduce the problem to a finite system of algebraic equations. Solutions are found which exhibit a rich variety of behaviour including primary, secondary and multiple bifurcation.

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Mathematics Subject Classification: Primary: 37G40, 76B15; Secondary: 34G56.

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