This article is
- freely available
Symmetries and (Related) Recursion Operators of Linear Evolution Equations
Dipartimento di Fisica “E. Fermi” dell’Universit`a di Pisa and INFN, sez. di Pisa, Largo B. Pontecorvo 3, Ed. B-C, I-56127–Pisa, Italy
Received: 28 December 2009; in revised form: 26 January 2010 / Accepted: 29 January 2010 / Published: 5 February 2010
Abstract: Significant cases of time-evolution equations, the linear Schr¨odinger and the Fokker–Planck equation are considered. It is known that equations of this type can be transformed, in some cases, into a highly simplified form. The properties of these equations in their initial and their simplified form are compared, showing in particular that this transformation partially prevents a clear understanding and a full application of the (physically relevant) notion of the so-called step up/down operators. These operators are shown to be recursion operators, related to the Lie point symmetries of the equations, which are also carefully discussed.
Keywords: recursion operators; step up/down operators; Lie point symmetries; Schrödinger equation; Fokker–Planck equation
Article StatisticsClick here to load and display the download statistics.
Notes: Multiple requests from the same IP address are counted as one view.
Cite This Article
MDPI and ACS Style
Cicogna, G. Symmetries and (Related) Recursion Operators of Linear Evolution Equations. Symmetry 2010, 2, 98-111.
Cicogna G. Symmetries and (Related) Recursion Operators of Linear Evolution Equations. Symmetry. 2010; 2(1):98-111.
Cicogna, Giampaolo. 2010. "Symmetries and (Related) Recursion Operators of Linear Evolution Equations." Symmetry 2, no. 1: 98-111.