An Extended Modified Kadomtsov-Petviashvili Equation: Ermakov-Painlev\'e II Symmetry Reduction with Moving Boundary Application
Exactly Solvable and Integrable Systems
2026-04-08 v2 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.2603.16520,
title = {An Extended Modified Kadomtsov-Petviashvili Equation: Ermakov-Painlev\'e II Symmetry Reduction with Moving Boundary Application},
author = {Colin Rogers and Pablo Amster},
journal= {arXiv preprint arXiv:2603.16520},
year = {2026}
}