Moving boundary problems for a novel extended mKdV equation. Application of Ermakov-Painlevé II symmetry reduction

Fuente: arXiv
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Main Authors: Rogers, Colin, Briozzo, Adriana C.
Format: Preprint
Published: 2025
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author Rogers, Colin
Briozzo, Adriana C.
author_facet Rogers, Colin
Briozzo, Adriana C.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2511_03356
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Moving boundary problems for a novel extended mKdV equation. Application of Ermakov-Painlevé II symmetry reduction
Rogers, Colin
Briozzo, Adriana C.
Analysis of PDEs
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.
title Moving boundary problems for a novel extended mKdV equation. Application of Ermakov-Painlevé II symmetry reduction
topic Analysis of PDEs
url https://arxiv.org/abs/2511.03356