Erik Wahlen: Large-amplitude solitary waves for the Whitham equation

In the 1960’s G. B. Whitham suggested a non-local version of the KdV equation as a model for water waves. Unlike the KdV equation it is not integrable, but it has certain other advantages. In particular, it has the same dispersion relation as the full water wave problem and it allows for wave breaking. The existence of a highest, cusped periodic wave was recently proved using global bifurcation theory. I will discuss the same problem for solitary waves. This presents several new challenges.

Joint work with T. Truong (Lund) and M. Wheeler (Bath).