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

摘要: We consider the problem of performing preliminary “symmetry classification” a class 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 “geometrical” characterization relevant system equations determining symmetries. Two detailed examples will elucidate idea procedure: first concerns nonlinear Laplace-type equation, second generalization equation (the Grad–Schluter–Shafranov equation) which is used magnetohydrodynamics.