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.
2008
Cicogna, Giampaolo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/122715
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