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arXiv · 2603.16520

An Extended Modified Kadomtsov-Petviashvili Equation: Ermakov-Painlev\'e II Symmetry Reduction with Moving Boundary Application

Colin Rogers·Pablo Amster
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Abstract

Here, a novel 2+1-dimensional nonlinear evolution equation with temporal modulation is introduced which admits integrable Ermakov-Painlev\'e 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-Painlev\'e II symmetry reduction applicable to certain moving boundary problems.

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Colin Rogers, Pablo Amster. 2026-03-17. An Extended Modified Kadomtsov-Petviashvili Equation: Ermakov-Painlev\'e II Symmetry Reduction with Moving Boundary Application. https://doi.org/10.46298/ocnmp.17767

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