Symmetry Reductions and Exact Solutions of a class of Nonlinear Heat Equations
| dc.creator | Clarkson, Peter A. | |
| dc.creator | Mansfield, Elizabeth L. | |
| dc.date | 1993-06-16 | |
| dc.date.accessioned | 2026-07-07T09:17:45Z | |
| dc.date.available | 2026-07-07T09:17:45Z | |
| dc.description | Classical and nonclassical symmetries of the nonlinear heat equation $$u_t=u_{xx}+f(u),\eqno(1)$$ are considered. The method of differential Gröbner bases is used both to find the conditions on $f(u)$ under which symmetries other than the trivial spatial and temporal translational symmetries exist, and to solve the determining equations for the infinitesimals. A catalogue of symmetry reductions is given including some new reductions for the linear heat equation and a catalogue of exact solutions of (1) for cubic $f(u)$ in terms of the roots of $f(u)=0$. | |
| dc.description | Latex file 32 pages, 13 figures available from author | |
| dc.identifier | https://arxiv.org/abs/solv-int/9306002 | |
| dc.identifier | http://arxiv.org/abs/solv-int/9306002 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/153783 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | Symmetry Reductions and Exact Solutions of a class of Nonlinear Heat Equations | |
| dc.type | text |