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.
European Journal of Applied Mathematics
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 Mathematics, 30(4), 756–790. https://doi.org/10.1017/S0956792518000396