Uniqueness of the pendent drop of infinite length

TL;DR

This paper proves the uniqueness of an infinite-length axisymmetric solution to the capillary equation by viewing it as a perturbation of an integrable system and applying an elementary perturbation argument.

Contribution

It establishes the first rigorous proof of the uniqueness of the infinite-length pendent drop solution in capillarity theory.

Findings

Uniqueness of the infinite-length axisymmetric solution is proven.

Capillary equation can be approximated as a perturbation of an integrable system.

Elementary perturbation methods are effective for proving solution uniqueness.

Abstract

We prove the uniqueness of the infinite length axisymmetric solution to the capillary equation. We observe that capillary equation can be viewed, at large depth, as a perturbation of an integrable two-dimensional differential system. Uniqueness is then proved by an elementary perturbation argument.