Journal article
Periodic travelling interfacial hydroelastic waves with or without mass II: Multiple bifurcations and ripples
European journal of applied mathematics, v 30(4), pp 756-790
Aug 2019
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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.
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Details
- Title
- Periodic travelling interfacial hydroelastic waves with or without mass II: Multiple bifurcations and ripples
- Creators
- Benjamin F Akers - U.S. Air Force Institute of TechnologyDavid M Ambrose - Drexel University, MathematicsDavid W Sulon - Drexel University, Mathematics
- Publication Details
- European journal of applied mathematics, v 30(4), pp 756-790
- Publisher
- Cambridge University Press; Cambridge, UK
- Number of pages
- 35
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000473322600005
- Scopus ID
- 2-s2.0-85049829753
- Other Identifier
- 991014878334104721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics, Applied