Large amplitude edge waves are shown to be modified by nonlinear effects in a way very similar to surface waves in deep water (Stokes, 1847); trapped harmonics tend to sharpen the wave crests and the natural frequency increases with wave amplitude, progressive edge waves propagating faster at large amplitude. A standing edge wave exhibits additional properties due to interaction between its two constituent progressive waves....
Guza, R. T., and A. J. Bowen. 1976. "Finite amplitude edge waves." Journal of Marine Research 34, (2). https://elischolar.library.yale.edu/journal_of_marine_research/1359