Erik Wahlén

I will discuss recent progress in the theory of solitary water waves
with surface tension. The mathematical model involves the
incompressible Euler equations with a free boundary. In the
two-dimensional case it is well-known that there are small-amplitude
solitary waves which to leading order are governed by the
Korteweg-de Vries equation, as well as waves which to
leading order look like wave packets governed by the nonlinear
Schrödinger equation. I will discuss three-dimensional
analogues of these waves, which are constructed using
variational methods and dynamical systems theory.