So called λ-symmetries were introduced by Muriel and Romero, and geometrically characterized by Pucci and Saccomandi [8, 12], in the ODE case. We extend them to the PDE framework. In this context the central object is a horizontal one-form µ, and we speak of µ-prolongations of vector fields and µ-symmetries of PDEs. The latter are as good as standard symmetries in providing symmetry reduction of PDEs (or systems thereof) and explicit invariant solutions.
PDEs reduction and λ-symmetries / G. Gaeta, P. Morando. - In: NOTE DI MATEMATICA. - ISSN 1123-2536. - 23:2(2004), pp. 33-73. [10.1285/i15900932v23n2p33]
PDEs reduction and λ-symmetries
G. GaetaPrimo
;P. MorandoUltimo
2004
Abstract
So called λ-symmetries were introduced by Muriel and Romero, and geometrically characterized by Pucci and Saccomandi [8, 12], in the ODE case. We extend them to the PDE framework. In this context the central object is a horizontal one-form µ, and we speak of µ-prolongations of vector fields and µ-symmetries of PDEs. The latter are as good as standard symmetries in providing symmetry reduction of PDEs (or systems thereof) and explicit invariant solutions.
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