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

Giampaolo Cicogna
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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-Schlüter-Shafranov equation) which is used in magnetohydrodynamics.

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Giampaolo Cicogna. 2007-02-02. Symmetry classification of quasi-linear PDE's containing arbitrary functions. https://arxiv.org/abs/math-ph/0702008

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