Document Type

Article

Publication Date

8-5-2019

Abstract

In a prior work, the authors proved a global bifurcation theorem for spatially periodic interfacial hydroelastic traveling waves on infinite depth, and computed such traveling waves. The formulation of the traveling 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 traveling waves in both of these situations. We compute the waves numerically as well, in both the resonant and non-resonant cases.

Comments

Sourced from the e-print version 2, at arxiv.org.
arXiv:1709.08076v2 [math.AP] ; https://arxiv.org/abs/1709.08076. Submitted to arXiv on 23 Sep 2017 (v1); revised 5 Jun 2018

The version of record at Cambridge: https://doi.org/10.1017/S0956792518000396

Publication Date refers to the version of record.

DOI

Akers, B. F., Ambrose, D. M., & Sulon, D. W. (2019). Periodic traveling interfacial hydroelastic waves with or without mass II: Multiple bifurcations and ripples. European Journal of Applied Mathematic, 30(4), 756–790. https://doi.org/https://doi.org/10.1017/S0956792518000396

Source Publication

European Journal of Applied Mathematics

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Mathematics Commons

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