An Extended Modified Kadomtsov-Petviashvili Equation: Ermakov-Painlevé II Symmetry Reduction with Moving Boundary Application

Here, a novel 2+1-dimensional nonlinear evolution equation with temporal modulation is introduced which admits integrable Ermakov-Painlevé II symmetry reduction. Application is made to obtain exact solution to a class of Stefan-type moving boundary problems for this 2+1-dimensional nonlinear evolution equation. Involutory transformations with origin in autonomisation of certain Ermakov-type coupled systems are extended to 2+1-dimensions and applied to derive a wide 2+1-dimensional class with temporal modulation and which inherits the property of admittance of such hybrid Ermakov-Painlevé II symmetry reduction applicable to certain moving boundary problems.