No pure capillary solitary waves exist in 2D finite depth

TL;DR

This paper proves that under classical physical assumptions, there are no solitary wave solutions in two-dimensional finite depth capillary water wave equations, resolving a long-standing existence question.

Contribution

It establishes a rigorous non-existence result for solitary waves in 2D finite depth capillary water waves, a problem previously unresolved.

Findings

No solitary wave solutions exist in 2D finite depth capillary water waves.

The proof closes the existence/non-existence problem for these waves.

Results hold under classical assumptions of incompressibility and irrotationality.

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.