Conservation laws for a generalized seventh order KdV equation
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911773496442880 |
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| author | Bruzón, María de los Santos Márquez, Almudena del Pilar Garrido, Tamara María Recio, Elena de la Rosa, Rafael |
| author_facet | Bruzón, María de los Santos Márquez, Almudena del Pilar Garrido, Tamara María Recio, Elena de la Rosa, Rafael |
| contents | In this paper, by applying the multiplier method we obtain a complete classification of low-order local conservation laws for a generalized seventh-order KdV equation depending on seven arbitrary nonzero parameters. We apply the Lie method in order to classify all point symmetries admitted by the equation in terms of the arbitrary parameters. We find that there are no special cases of the parameters for which the equation admits extra symmetries, other than those that can be found by inspection (scaling symmetry and space and time translation symmetries). We consider the reduced ordinary differential equations and we determined all integrating factors of the reduced equation from the combined $x$- and $t$- translation symmetries. Finally, we observe that all integrating factors arise by reduction of the low-order multipliers of the generalized seventh-order KdV equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05341 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conservation laws for a generalized seventh order KdV equation Bruzón, María de los Santos Márquez, Almudena del Pilar Garrido, Tamara María Recio, Elena de la Rosa, Rafael Exactly Solvable and Integrable Systems Analysis of PDEs In this paper, by applying the multiplier method we obtain a complete classification of low-order local conservation laws for a generalized seventh-order KdV equation depending on seven arbitrary nonzero parameters. We apply the Lie method in order to classify all point symmetries admitted by the equation in terms of the arbitrary parameters. We find that there are no special cases of the parameters for which the equation admits extra symmetries, other than those that can be found by inspection (scaling symmetry and space and time translation symmetries). We consider the reduced ordinary differential equations and we determined all integrating factors of the reduced equation from the combined $x$- and $t$- translation symmetries. Finally, we observe that all integrating factors arise by reduction of the low-order multipliers of the generalized seventh-order KdV equation. |
| title | Conservation laws for a generalized seventh order KdV equation |
| topic | Exactly Solvable and Integrable Systems Analysis of PDEs |
| url | https://arxiv.org/abs/2402.05341 |