*Title*: **Traveling waves in a full-dispersion gravity-capillary shallow water model**

*Abstract*: In this talk, I will present new results concerning the existence and dynamics of traveling waves in a unidirectional Whitham equation with gravity and capillary effects taken into account. It is well known that the full gravity-capillary water wave problem exhibits many interesting solutions, such as solitary waves of elevation and depression, multi-bump periodic patterns (so-called ``Wilton ripplesâ€ť), and generalized solitary waves consisting of a localized core connecting to very small periodic oscillations at spatial infinity. Our goal here is to see how each of these types of solutions manifest in the aforementioned Whitham equation, and to see what we can say concerning their stability.

CAM Seminar Fall 2018