Small-amplitude steady water waves with critical layers: Non-symmetric waves

The problem for two-dimensional steady water waves with vorticity is considered. Using methods of spatial dynamics, we reduce the problem to a finite dimensional Hamiltonian system. The reduced system describes all small-amplitude solutions of the problem and, as an application, we give a proof of the existence of non-symmetric steady water waves whenever the number of roots of the dispersion equation is greater than one. (C) 2019 Published by Elsevier Inc.Funding Agencies|Swedish Research Council (VR) [2017-03837]