We extend Painlevé IV model by adding quadratic terms to its Hamiltonian obtaining two classes of models (coalescence and deformation) that interpolate between Painlevé IV and II equations for special limits of the underlying ...

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 ...

This paper rst discusses irreducibility of a Painlev e equation P. We explain how the Painlev e property is helpful for the computation of special classical and algebraic solutions. As in a paper of Morales-Ruiz we ...

A two-point Neumann boundary value problem for a two ion electro-diffusion model reducible to the Painlevé II equation is investigated. The problem is unconventional in that the model equation involves yet-to-be determined ...

In prior work, a series of two-point boundary value problems have been investigated for a steady state two-ion electro-diffusion model system in which the sum of the valencies ν+ and ν− is zero. In that case, reduction is ...