Symmetry classification of quasi-linear PDE's containing arbitrary functions
Mathematical Physics
2007-05-23 v1 math.MP
Abstract
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.
Cite
@article{arxiv.math-ph/0702008,
title = {Symmetry classification of quasi-linear PDE's containing arbitrary functions},
author = {Giampaolo Cicogna},
journal= {arXiv preprint arXiv:math-ph/0702008},
year = {2007}
}
Comments
15 pages; to be published in Nonlinear Dynamics