# Analysis Seminar

#### Solitary Water Waves in Three Dimensions

**Speaker:**
Erik Wahlen, University of Lund

**Location:**
Warren Weaver Hall 1302

**Date:**
Thursday, April 10, 2014, 11 a.m.

**Synopsis:**

I will discuss some existence results for solitary waves with surface tension on a three-dimensional layer of water of finite depth. The waves are fully localized in the sense that they converge to the undisturbed state of the water in every horizontal direction. The existence proofs are of variational nature and different methods are used depending on whether the surface tension is weak or strong. In the case of strong surface tension, the existence proof also gives some information about the stability of the waves. The solutions are to leading order described by the Kadomtsev-Petviashvili equation (for strong surface tension) or the Davey-Stewartson equation (for weak surface tension). These model equations play an important role in the theory.