Moving boundary problems with Ermakov symmetry reduction: nonlinear superposition principle and reciprocal transformation applications

2025/08/24 by Rogers, Colin, Briozzo, Adriana C.
#35R37 #80A22 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.17421

Abstract

Moving boundary problems of Stefan-type for a novel third order nonlinear evolution equation with temporal modulation are here shown to be amenable to exact Airy-type solution via a classical Ermakov equation with its admitted nonlinear superposition principle. Application of the latter together with a class of involutory transformations sets the original moving boundary problem in a wide class with temporal modulation. As an appendix, reciprocally associated exactly solvable moving boundary problems are derived.

Citations

• A Novel Ermakov–Painlevé II System: ‐Dimensional Coupled NLS and Elastodynamic Reductions
• The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid

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