Symmetry classification of quasi-linear PDE's containing arbitrary functions
Abstract
Description
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-Schlüter-Shafranov equation) which is used in magnetohydrodynamics.
15 pages; to be published in Nonlinear Dynamics
15 pages; to be published in Nonlinear Dynamics