Two sequences of fully-nonlinear evolution equations and their symmetry properties
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911225354387456 |
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| author | Euler, Marianna Euler, Norbert |
| author_facet | Euler, Marianna Euler, Norbert |
| contents | We obtain the complete Lie point symmetry algebras of two sequences of odd-order evolution equations. This includes equations that are fully-nonlinear, i.e. nonlinear in the highest derivative. Two of the equations in the sequences have recently been identified as symmetry-integrable, namely a 3rd-order equation and a 5th-order equation [Open Communications in Nonlinear Mathematical Physics, Special Issue in honour of George W Bluman, ocnmp:15938, 1--15, 2025]. These two examples provided the motivation for the current study. The Lie-Bäcklund symmetries and the consequent symmetry-integrability of the equations in the sequences are also discussed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_05535 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two sequences of fully-nonlinear evolution equations and their symmetry properties Euler, Marianna Euler, Norbert Exactly Solvable and Integrable Systems We obtain the complete Lie point symmetry algebras of two sequences of odd-order evolution equations. This includes equations that are fully-nonlinear, i.e. nonlinear in the highest derivative. Two of the equations in the sequences have recently been identified as symmetry-integrable, namely a 3rd-order equation and a 5th-order equation [Open Communications in Nonlinear Mathematical Physics, Special Issue in honour of George W Bluman, ocnmp:15938, 1--15, 2025]. These two examples provided the motivation for the current study. The Lie-Bäcklund symmetries and the consequent symmetry-integrability of the equations in the sequences are also discussed. |
| title | Two sequences of fully-nonlinear evolution equations and their symmetry properties |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2509.05535 |