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.
Symmetry classification of quasi-linear PDE's containing arbitrary functions
CICOGNA, GIAMPAOLO
2008-01-01
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-Schluter-Shafranov equation) which is used in magnetohydrodynamics.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.