Data di Pubblicazione:
2005
Citazione:
Asymptotic scaling symmetries for nonlinear PDEs / G. Gaeta, R. Mancinelli. - In: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS. - ISSN 0219-8878. - 2:6(2005), pp. 1081-1114.
Abstract:
In some cases, solutions to nonlinear PDEs happen to be asymptotically (for large x and/or t) invariant under a group G which is not a symmetry of the equation. After recalling the geometrical meaning of symmetries of differential equations — and solution-preserving maps — we provide a precise definition of asymptotic symmetries of PDEs; we deal in particular, for ease of discussion and physical relevance, with scaling and translation symmetries of scalar equations. We apply the general discussion to a class of "Richardson-like" anomalous diffusion and reaction-diffusion equations, whose solution are known by numerical experiments to be asymptotically scale invariant; we obtain an analytical explanation of the numerically observed asymptotic scaling properties. We also apply our method to a different class of anomalous diffusion equations, relevant in optical lattices. The methods developed here can be applied to more general equations, as shown by their geometrical construction.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Asymptotic invariance; Invariant solutions; Symmetry
Elenco autori:
G. Gaeta, R. Mancinelli
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