Symmetries and (Related) Recursion Operators of Linear Evolution Equations
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2010-02-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/2/1/98/ |
| _version_ | 1798002816364576768 |
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| author | Giampaolo Cicogna |
| author_facet | Giampaolo Cicogna |
| author_sort | Giampaolo Cicogna |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T11:58:15Z |
| format | Article |
| id | doaj.art-2bde1b4324fd49e48d47bc91c2052ddb |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T11:58:15Z |
| publishDate | 2010-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-2bde1b4324fd49e48d47bc91c2052ddb2022-12-22T04:24:58ZengMDPI AGSymmetry2073-89942010-02-01219811110.3390/sym2010098Symmetries and (Related) Recursion Operators of Linear Evolution EquationsGiampaolo CicognaSignificant 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.http://www.mdpi.com/2073-8994/2/1/98/recursion operatorsstep up/down operatorsLie point symmetriesSchrödinger equationFokker–Planck equation |
| spellingShingle | Giampaolo Cicogna Symmetries and (Related) Recursion Operators of Linear Evolution Equations Symmetry recursion operators step up/down operators Lie point symmetries Schrödinger equation Fokker–Planck equation |
| title | Symmetries and (Related) Recursion Operators of Linear Evolution Equations |
| title_full | Symmetries and (Related) Recursion Operators of Linear Evolution Equations |
| title_fullStr | Symmetries and (Related) Recursion Operators of Linear Evolution Equations |
| title_full_unstemmed | Symmetries and (Related) Recursion Operators of Linear Evolution Equations |
| title_short | Symmetries and (Related) Recursion Operators of Linear Evolution Equations |
| title_sort | symmetries and related recursion operators of linear evolution equations |
| topic | recursion operators step up/down operators Lie point symmetries Schrödinger equation Fokker–Planck equation |
| url | http://www.mdpi.com/2073-8994/2/1/98/ |
| work_keys_str_mv | AT giampaolocicogna symmetriesandrelatedrecursionoperatorsoflinearevolutionequations |