No pure capillary solitary waves exist in 2D finite depth

Abstract

We prove that the 2D finite depth capillary water wave equations admit no solitary wave solutions. This closes the existence/non-existence problem for solitary water waves in 2D, under the classical assumptions of incompressibility and irrotationality, and with the physical parameters being gravity, surface tension and the fluid depth.

Cited by in corpus (1)

• Two dimensional solitary water waves with constant vorticity, Part I: the deep gravity case