Wilton Ripples in Weakly Nonlinear Dispersive Models of Water Waves: Existence and Analyticity of Solution Branches
Traveling waves on the surface of the ocean play an important role in many oceanographic processes which necessitates a detailed quantitative understanding of their properties. The water wave equations, which govern the free-surface evolution of an ideal fluid, are the most successful model for this phenomena, but are exceedingly difficult to analyze due to their strongly nonlinear character and the fact that they are posed on a domain with moving boundary. For this reason, weakly nonlinear dispersive models are an essential tool for practitioners, and in this contribution, we study traveling wave solutions of a broad class of such models.
Akers, B., Nicholls, D.P. Wilton Ripples in Weakly Nonlinear Dispersive Models of Water Waves: Existence and Analyticity of Solution Branches. Water Waves 3, 25–47 (2021). https://doi.org/10.1007/s42286-020-00034-w