Painlev\'e structure of a multi-ion electrodiffusion system

TL;DR

This paper analyzes a multi-ion electrodiffusion system to identify parameter conditions for single-valued solutions, using Painleve' analysis, and finds explicit solutions in terms of special functions.

Contribution

It applies Painleve' analysis to a complex electrodiffusion model to determine parameter regimes with explicit solutions, advancing understanding of its integrability.

Findings

Parameters for single-valued solutions are identified.

Solutions can be expressed via Painleve' transcendents or elliptic functions.

The system's integrability conditions are characterized.

Abstract

A nonlinear coupled system descriptive of multi-ion electrodiffusion is investigated and all parameters for which the system admits a single-valued general solution are isolated. This is achieved \textit{via} a method initiated by Painleve' with the application of a test due to Kowalevski and Gambier. The solutions can be obtained explicitly in terms of Painleve' transcendents or elliptic functions.