The Method of ${\cal M}_{n}$-Extension: The KdV Equation
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915095174447104 |
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| author | Gürses, Metin Pekcan, Aslı |
| author_facet | Gürses, Metin Pekcan, Aslı |
| contents | In this work we generalize ${\cal M}_{2}$-extension that has been introduced recently. For illustration we use the KdV equation. We present five different ${\cal M}_{3}$-extensions of the KdV equation and their recursion operators. We give a compact form of ${\cal M}_{n}$-extension of the KdV equation and recursion operator of the coupled KdV system. The method of ${\cal M}_{n}$-extension can be applied to any integrable scalar equation to obtain integrable multi-field system of equations. We also present unshifted and shifted nonlocal reductions of an example of ${\cal M}_{3}$-extension of KdV. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04673 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Method of ${\cal M}_{n}$-Extension: The KdV Equation Gürses, Metin Pekcan, Aslı Exactly Solvable and Integrable Systems In this work we generalize ${\cal M}_{2}$-extension that has been introduced recently. For illustration we use the KdV equation. We present five different ${\cal M}_{3}$-extensions of the KdV equation and their recursion operators. We give a compact form of ${\cal M}_{n}$-extension of the KdV equation and recursion operator of the coupled KdV system. The method of ${\cal M}_{n}$-extension can be applied to any integrable scalar equation to obtain integrable multi-field system of equations. We also present unshifted and shifted nonlocal reductions of an example of ${\cal M}_{3}$-extension of KdV. |
| title | The Method of ${\cal M}_{n}$-Extension: The KdV Equation |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2501.04673 |