Title: Traveling wave solutions of the capillary-gravity Whitham equation

Abstract: "Whitham'' equations have enjoyed a recent resurgence of popularity as models for free surface fluid flows. They are, roughly speaking, obtained by using the full linear part of the appropriate Euler equation together with a simpler "KdV"-type nonlinearity. Generalized solitary waves are traveling wave solutions which are the superposition of a classical solitary wave with a "small beyond all orders" periodic wave. Such waves are known to exist for the full capillary-gravity wave problem and in this talk we discuss recent work on establishing their existence for the "Whithamized" version. This work is done in collaboration with Atanas Stefanov and Mat Johnson (both at Kansas).

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