Kinetic, potential and surface tension energies of solitary waves in deep water

TL;DR

This paper derives an exact energy relation for solitary waves in deep water, revealing their non-existence without surface tension effects when gravity acts oppositely to natural conditions.

Contribution

It provides a novel exact relation among energies of solitary waves and demonstrates their non-existence under certain unphysical gravity conditions.

Findings

Exact energy relation for solitary waves in deep water

Non-existence of solitary waves without surface tension under reversed gravity

Theoretical insight into wave energy dynamics

Abstract

We present an exact relation among the kinetic, potential and surface tension energies of a solitary wave in deep water in all dimensions. We deduce its non-existence in the absence of the effects of surface tension, provided that gravity acts in a direction opposite to what is physically realistic.