On mKdV and associated classes of moving boundary problems: reciprocal connections-Reference-Cited by-同舟云学术

On mKdV and associated classes of moving boundary problems: reciprocal connections

Published:2023-08 Issue:8 Volume:58 Page:1633-1640
ISSN:0025-6455
Container-title:Meccanica
language:en
Short-container-title:Meccanica

Author:

Rogers Colin^ORCID

Abstract

AbstractA class of Stefan-type moving boundary problems for the canonical modified Korteweg–de Vries (mKdV) equation of soliton theory is solved via application of a similarity reduction to Painlevé II which involves Airy’s equation. A reciprocal transformation is applied to derive a linked class of solvable moving boundary problems for a basic Casimir member of a compacton hierarchy. Application of a class of involutory transformations with origin in an autonomisation procedure for the Ermakov–Ray–Reid system is then used to isolate novel solvable moving boundary problems for Ermakov-modulated mkdV equations.

Funder

University of New South Wales

Publisher

Springer Science and Business Media LLC

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Link

https://link.springer.com/content/pdf/10.1007/s11012-023-01696-9.pdf

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