A novel extension of the canonical solitonic mKdV equation is introduced which admits hybrid Ermakov-Painlevé II symmetry reduction. Application of the latter is made to obtain exact solution of Airy-type to a class of moving boundary problems of Stefan kind for this extended mKdV equation. A reciprocal transformation is then applied to the latter to generate an associated exactly solvable class of moving boundary problems for an extension of a base Casimir member of a compacton hierachy. The extended mKdV equation is shown to be embedded in a range of nonlinear evolution equations with temporal modulation as determined via the action of a class of involutory transformations with origin in Ermakov theory. Associated temporal modulation for the hybrid mKdV and KdV equation as embedded in the classical solitonic Gardner equation is delimited.

15 pages