On a Painlev6 I1 Model in Steady Electrolysis: Application of a Backlund Transformation

A model equation of PainlevC I1 type was introduced by Bass in 1964 in connection with a boundary value problem which describes the electric field distribution in a region x > 0 occupied by an electrolyte. This is possibly the earliest explicit physical application of a PainlevC equation to be found in the literature. Here we return to this problem informed by the subsequent discovery of a Backlund transformation for PainlevC 11. This enables us to construct exact representations for the electric field and ion distributions for boundary value problems wherein the ratio of fluxes of the positive and negative ions at the boundary adopts one of an infinite sequence of values