Moving boundary problems for a novel extended mKdV equation. Application of Ermakov-Painlevé II symmetry reduction
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911298184282112 |
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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 |