Numerical studies of two-dimensional hydroelastic periodic and generalised solitary waves

Hydroelastic waves propagating at a constant velocity at the surface of a fluid are considered. The flow is assumed to be two-dimensional and potential. Gravity is included in the dynamic boundary condition. The fluid is bounded above by an elastic sheet which is described by the Plotnikov-Toland model. Fully nonlinear solutions are computed by a series truncation method. The findings generalised previous results where the sheet was described by a simplified model known as the Kirchhoff-Love model. Periodic and generalised solitary waves are computed. The results strongly suggest that there are no true solitary waves (i.e., solitary waves characterised by a flat free surface in the far field). Detailed comparisons with results obtained with the Kirchhoff-Love model and for the related problem of gravity capillary waves are also presented.