Journal article 850 views
Additional symmetries of generalized integrable hierarchies
Journal of Physics A: Mathematical and General, Volume: "A27", Issue: 13, Pages: 4629 - 4644
Swansea University Author:
Timothy Hollowood
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DOI (Published version): 10.1088/0305-4470/27/13/036
Abstract
The non-isospectral symmetries of a general class of integrable hierarchies are found, generalizing the Galilean and scaling symmetries of the Korteweg--de Vries equation and its hierarchy. The symmetries arise in a very natural way from the semi-direct product structure of the Virasoro algebra and...
| Published in: | Journal of Physics A: Mathematical and General |
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| ISSN: | 0305-4470 1361-6447 |
| Published: |
1993
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| Online Access: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa28585 |
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| Abstract: |
The non-isospectral symmetries of a general class of integrable hierarchies are found, generalizing the Galilean and scaling symmetries of the Korteweg--de Vries equation and its hierarchy. The symmetries arise in a very natural way from the semi-direct product structure of the Virasoro algebra and the affine Kac--Moody algebra underlying the construction of the hierarchy. In particular, the generators of the symmetries are shown to satisfy a subalgebra of the Virasoro algebra. When a tau-function formalism is available, the infinitesimal symmetries act directly on the tau-functions as moments of Virasoro currents. Some comments are made regarding the r\~ole of the non-isospectral symmetries and the form of the string equations in matrix-model formulations of quantum gravity in two-dimensions and related |
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| College: |
Faculty of Science and Engineering |
| Issue: |
13 |
| Start Page: |
4629 |
| End Page: |
4644 |