We study the motion of an interface between two irrotational, incompressiblefluids, with elastic bending forces present; this is the hydroelastic waveproblem. We prove a global bifurcation theorem for the existence of families ofspatially periodic traveling waves on infinite depth. Our traveling waveformulation uses a parameterized curve, in which the waves are able to havemulti-valued height. This formulation and the presence of the elastic bendingterms allows for the application of an abstract global bifurcation theorem of"identity plus compact" type. We furthermore perform numerical computations ofthese families of traveling waves, finding that, depending on the choice ofparameters, the curves of traveling waves can either be unbounded, reconnect totrivial solutions, or end with a wave which has a self-intersection. Ouranalytical and computational methods are able to treat in a unified way thecases of positive or zero mass density along the sheet, the cases ofsingle-valued or multi-valued height, and the cases of single-fluid orinterfacial waves.
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