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-Schluter-Shafranov equation) which is used in magnetohydrodynamics.
|Titolo:||Symmetry classification of quasi-linear PDE's containing arbitrary functions|
|Anno del prodotto:||2008|
|Digital Object Identifier (DOI):||10.1007/s11071-007-9212-7|
|Appare nelle tipologie:||1.1 Articolo in rivista|