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Periodic travelling interfacial hydroelastic waves with or without mass II: Multiple bifurcations and ripples

Published online by Cambridge University Press:  10 July 2018

BENJAMIN F. AKERS
Affiliation:
Department of Mathematics and Statistics, Air Force Institute of Technology, 2950 Hobson Way, WPAFB, OH 45433, USA email: benjamin.akers@afit.edu
DAVID M. AMBROSE
Affiliation:
Department of Mathematics, Drexel University, 3141 Chestnut St., Philadelphia, PA 19104, USA email: dma68@drexel.edu, dws57@drexel.edu
DAVID W. SULON
Affiliation:
Department of Mathematics, Drexel University, 3141 Chestnut St., Philadelphia, PA 19104, USA email: dma68@drexel.edu, dws57@drexel.edu

Abstract

In a prior work, the authors proved a global bifurcation theorem for spatially periodic interfacial hydroelastic travelling waves on infinite depth, and computed such travelling waves. The formulation of the travelling wave problem used both analytically and numerically allows for waves with multi-valued height. The global bifurcation theorem required a one-dimensional kernel in the linearization of the relevant mapping, but for some parameter values, the kernel is instead two-dimensional. In the present work, we study these cases with two-dimensional kernels, which occur in resonant and non-resonant variants. We apply an implicit function theorem argument to prove existence of travelling waves in both of these situations. We compute the waves numerically as well, in both the resonant and non-resonant cases.

Type
Papers
Copyright
Copyright © Cambridge University Press 2018

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