Miura-Reciprocal Transformation and Symmetries for the Spectral Problems of KdV and mKdV
[EN] We present reciprocal transformations for the spectral problems of Korteveg de Vries (KdV) and modified Korteveg de Vries (mKdV) equations. The resulting equations, RKdV (reciprocal KdV) and RmKdV (reciprocal mKdV), are connected through a transformation that combines both Miura and reciprocal...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | España |
| Recursos: | Universidad de Salamanca (USAL) |
| Repositorio: | GREDOS. Repositorio Institucional de la Universidad de Salamanca |
| OAI Identifier: | oai:gredos.usal.es:10366/169891 |
| Acesso em linha: | http://hdl.handle.net/10366/169891 |
| Access Level: | acceso abierto |
| Palavra-chave: | Symmetry groups Conservation laws Partial differential equations 1202.20 Ecuaciones Diferenciales en derivadas Parciales |
| Resumo: | [EN] We present reciprocal transformations for the spectral problems of Korteveg de Vries (KdV) and modified Korteveg de Vries (mKdV) equations. The resulting equations, RKdV (reciprocal KdV) and RmKdV (reciprocal mKdV), are connected through a transformation that combines both Miura and reciprocal transformations. Lax pairs for RKdV and RmKdV are straightforwardly obtained by means of the aforementioned reciprocal transformations. We have also identified the classical Lie symmetries for the Lax pairs of RKdV and RmKdV. Non-trivial similarity reductions are computed and they yield non-autonomous ordinary differential equations (ODEs), whose Lax pairs are obtained as a consequence of the reductions. |
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