Symmetry classification of quasi-linear PDE’s containing arbitrary functions |
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Authors: | Giampaolo Cicogna |
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Institution: | (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 |
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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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Keywords: | Symmetry classification Quasi-linear PDE’ s Symmetry determining equations Generalized Laplace equation Grad– Schlüter– Shafranov equation |
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