Asymptotic scaling symmetries for nonlinear PDEs
| dc.creator | Gaeta, G. | |
| dc.creator | Mancinelli, R. | |
| dc.date | 2006-02-14 | |
| dc.date.accessioned | 2026-07-07T07:02:58Z | |
| dc.date.available | 2026-07-07T07:02:58Z | |
| dc.description | 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 clear by their geometrical construction. | |
| dc.identifier | https://arxiv.org/abs/math-ph/0602041 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0602041 | |
| dc.identifier | Int. J. Geom. Meth. Mod. Phys. 2 (2005), 1081-1114 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/108802 | |
| dc.subject | Mathematical Physics | |
| dc.title | Asymptotic scaling symmetries for nonlinear PDEs | |
| dc.type | text |