Symmetry Reductions and Exact Solutions of a class of Nonlinear Heat Equations
Abstract
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 $f(u)=0$.
 Publication:

arXiv eprints
 Pub Date:
 June 1993
 arXiv:
 arXiv:solvint/9306002
 Bibcode:
 1993solv.int..6002C
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 Latex file 32 pages, 13 figures available from author