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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | https://arxiv.org/abs/2512.12789 |
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| _version_ | 1866912794736066560 |
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| author | Garifullin, Rustem N. |
| author_facet | Garifullin, Rustem N. |
| contents | This paper examines the classification of hyperbolic equations. We study a class of equations of the form $$\frac{\partial^2 u}{\partial x\partial y}=F\left(\frac{\partial u}{\partial x},\frac{\partial u}{\partial y},u\right),$$ where $u(x,y)$ is the unknown function and $x,y$ are independent variables. The classification is based on the requirement for the existence of higher fifth-order symmetries. As a result, a list of four equations with the required conditions was obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12789 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hyperbolic equations with fifth-order symmetries Garifullin, Rustem N. Analysis of PDEs Exactly Solvable and Integrable Systems 37K10, 39A36 This paper examines the classification of hyperbolic equations. We study a class of equations of the form $$\frac{\partial^2 u}{\partial x\partial y}=F\left(\frac{\partial u}{\partial x},\frac{\partial u}{\partial y},u\right),$$ where $u(x,y)$ is the unknown function and $x,y$ are independent variables. The classification is based on the requirement for the existence of higher fifth-order symmetries. As a result, a list of four equations with the required conditions was obtained. |
| title | Hyperbolic equations with fifth-order symmetries |
| topic | Analysis of PDEs Exactly Solvable and Integrable Systems 37K10, 39A36 |
| url | https://arxiv.org/abs/2512.12789 |