From fully-nonlinear to semilinear evolution equations: two symmetry-integrable examples
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909709813940224 |
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| author | Euler, Marianna Euler, Norbert |
| author_facet | Euler, Marianna Euler, Norbert |
| contents | In this paper we derive two examples of fully-nonlinear symmetry-integrable evolution equations with algebraic nonlinearities, namely one class of 3rd-order equations and a 5th-order equation. To achieve this we study the equations' Lie-Bäcklund symmetries and apply multipotentialisations, hodograph transformations and generalised hodograph transformations to map the equations to known semilinear integrable evolution equations. As a result of this, we also obtain interesting symmetry-integrable quasilinear equations of order five and order seven, which we display explicitly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19070 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From fully-nonlinear to semilinear evolution equations: two symmetry-integrable examples Euler, Marianna Euler, Norbert Exactly Solvable and Integrable Systems In this paper we derive two examples of fully-nonlinear symmetry-integrable evolution equations with algebraic nonlinearities, namely one class of 3rd-order equations and a 5th-order equation. To achieve this we study the equations' Lie-Bäcklund symmetries and apply multipotentialisations, hodograph transformations and generalised hodograph transformations to map the equations to known semilinear integrable evolution equations. As a result of this, we also obtain interesting symmetry-integrable quasilinear equations of order five and order seven, which we display explicitly. |
| title | From fully-nonlinear to semilinear evolution equations: two symmetry-integrable examples |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2506.19070 |