Symmetry classification of quasi-linear PDE's containing arbitrary functions

Details Symmetry classification of quasi-linear PDE's containing arbitrary functions Symmetry classification of quasi-linear PDE's containing arbitrary functions

2007-02-02

arxiv.org/abs/math-ph/0702008v1

Physics

Mathematical Physics

15 pages; to be published in Nonlinear Dynamics

Scientific paper

We consider the problem of performing the preliminary "symmetry classification'' of a class of quasi-linear PDE's containing one or more arbitrary functions: we provide an easy condition involving these functions in order that nontrivial Lie point symmetries be admitted, and a "geometrical'' characterization of the relevant system of equations determining these symmetries. Two detailed examples will elucidate the idea and the procedure: the first one concerns a nonlinear Laplace-type equation, the second a generalization of an equation (the Grad-Schl\"uter-Shafranov equation) which is used in magnetohydrodynamics.

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