Solitary axisymmetric capillary water waves

We consider steady axisymmetric water waves subject to surface tension, where we study the free-boundary problem for domains close to an infinite cylinder. In the case of linear vorticity in radial direction and no swirl, we are able to prove existence of small solitary solutions of KdV-type. They bifurcate from laminar flows in a flat cylinder and the presence of vorticity is required for their existence. The proof relies on a spatial dynamics approach allowing for a center-manifold reduction, which reduces the problem to a finite-dimensional dynamical system. Homoclinic solutions of this system, which correspond to solitary wave solutions on the cylinder, are found using dynamical systems methods.

This is joint work with Dag Nilsson.