On a Ermakov-Painlevé II reduction in three-ion electrodiffusion: a Dirichlet boundary value problem

Abstract

Two-point boundary value problems of Dirichlet type are investigated for a ErmakovPainlev´e II equation which arises out of a reduction of a three-ion electrodiffusion Nernst-Planck model system. In addition, it is shown how Ermakov invariants may be employed to solve a hybrid Ermakov-Painlev´e II triad in terms of a solution of the single component integrable Ermakov-Painlev´e II reduction. The latter is related to the classical Painlev´e II equation.