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

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 $\mathit{\text{via}}$ 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.