Ermakov-Painleve' II Symmetry Reduction of a Class of Moving Boundary Problems for a Reciprocal Extended mKdV Equation

A reciprocal transformation is applied to link an integrable extension of the classical solitonic mKdV to a novel nonlinear evolution equation incorporating a source term. Application of Ermakov-Painleve’ II symmetry reduction is made to determine the exact solution to a class of associated moving boundary problems of Stefan-type.