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Additional symmetries of generalized integrable hierarchies / Joaquin Sanchez Guillen; J.Luis Miramontes; Timothy Hollowood

Journal of Physics A: Mathematical and General, Volume: "A27", Issue: 13, Pages: 4629 - 4644

Swansea University Author: Timothy, Hollowood

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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...

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Published in: Journal of Physics A: Mathematical and General
ISSN: 0305-4470 1361-6447
Published: 1993
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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
College: College of Science
Issue: 13
Start Page: 4629
End Page: 4644