Symmetry operators and generation of symmetry transformations of partial differential equations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866914125042417664 |
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| author | Papachristou, C. J. |
| author_facet | Papachristou, C. J. |
| contents | The study of symmetries of partial differential equations (PDEs) has been traditionally treated as a geometrical problem. Although geometrical methods have been proven effective with regard to finding infinitesimal symmetry transformations, they present certain conceptual difficulties in the case of matrix-valued PDEs; for example, the usual differential-operator representation of the symmetry-generating vector fields is not possible in this case. In this article an algebraic approach to the symmetry problem of PDEs - both scalar and matrix-valued - is described, based on abstract operators (characteristic derivatives) that admit a standard differential-operator representation in the case of scalar-valued PDEs. A number of examples are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1804_06303 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Symmetry operators and generation of symmetry transformations of partial differential equations Papachristou, C. J. Analysis of PDEs The study of symmetries of partial differential equations (PDEs) has been traditionally treated as a geometrical problem. Although geometrical methods have been proven effective with regard to finding infinitesimal symmetry transformations, they present certain conceptual difficulties in the case of matrix-valued PDEs; for example, the usual differential-operator representation of the symmetry-generating vector fields is not possible in this case. In this article an algebraic approach to the symmetry problem of PDEs - both scalar and matrix-valued - is described, based on abstract operators (characteristic derivatives) that admit a standard differential-operator representation in the case of scalar-valued PDEs. A number of examples are given. |
| title | Symmetry operators and generation of symmetry transformations of partial differential equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/1804.06303 |