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

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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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  1. Dipartimento di Fisica “E. Fermi” dell’Universitá di Pisa, and Istituto Nazionale di Fisica Nucleare, Sez. di Pisa, Largo B. Pontecorvo 3, Ed. B-C, I-56127, Pisa, Italy

    Giampaolo Cicogna

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  1. Giampaolo Cicogna
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Correspondence to Giampaolo Cicogna.

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Cicogna, G. Symmetry classification of quasi-linear PDE’s containing arbitrary functions. Nonlinear Dyn 51, 309–316 (2008). https://doi.org/10.1007/s11071-007-9212-7

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