Additional symmetries of generalized integrable hierarchies

Guillen, Joaquin Sanchez; Miramontes, J.Luis; Hollowood, Timothy

doi:10.1088/0305-4470/27/13/036

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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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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...

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Published in:	Journal of Physics A: Mathematical and General
ISSN:	0305-4470 1361-6447
Published:	1993
Online Access:	Check full text
URI:	https://cronfa.swan.ac.uk/Record/cronfa28585
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first_indexed	2016-06-03T19:16:32Z
last_indexed	2018-02-09T05:12:53Z
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spelling	2016-06-03T14:37:00.2811464 v2 28585 2016-06-03 Additional symmetries of generalized integrable hierarchies ea9ca59fc948276ff2ab547e91bdf0c2 0000-0002-3258-320X Timothy Hollowood Timothy Hollowood true false 2016-06-03 SPH 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 Journal Article Journal of Physics A: Mathematical and General "A27" 13 4629 4644 0305-4470 1361-6447 31 10 1993 1993-10-31 10.1088/0305-4470/27/13/036 http://inspirehep.net/record/359923 COLLEGE NANME Physics COLLEGE CODE SPH Swansea University 2016-06-03T14:37:00.2811464 2016-06-03T14:37:00.0627450 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Joaquin Sanchez Guillen 1 J.Luis Miramontes 2 Timothy Hollowood 0000-0002-3258-320X 3
title	Additional symmetries of generalized integrable hierarchies
spellingShingle	Additional symmetries of generalized integrable hierarchies Timothy Hollowood
title_short	Additional symmetries of generalized integrable hierarchies
title_full	Additional symmetries of generalized integrable hierarchies
title_fullStr	Additional symmetries of generalized integrable hierarchies
title_full_unstemmed	Additional symmetries of generalized integrable hierarchies
title_sort	Additional symmetries of generalized integrable hierarchies
author_id_str_mv	ea9ca59fc948276ff2ab547e91bdf0c2
author_id_fullname_str_mv	ea9ca59fc948276ff2ab547e91bdf0c2_***_Timothy Hollowood
author	Timothy Hollowood
author2	Joaquin Sanchez Guillen J.Luis Miramontes Timothy Hollowood
format	Journal article
container_title	Journal of Physics A: Mathematical and General
container_volume	"A27"
container_issue	13
container_start_page	4629
publishDate	1993
institution	Swansea University
issn	0305-4470 1361-6447
doi_str_mv	10.1088/0305-4470/27/13/036
college_str	Faculty of Science and Engineering
hierarchytype
hierarchy_top_id	facultyofscienceandengineering
hierarchy_top_title	Faculty of Science and Engineering
hierarchy_parent_id	facultyofscienceandengineering
hierarchy_parent_title	Faculty of Science and Engineering
department_str	School of Biosciences, Geography and Physics - Physics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Physics
url	http://inspirehep.net/record/359923
document_store_str	0
active_str	0
description	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
published_date	1993-10-31T03:34:49Z
_version_	1763751483156725760
score	11.036706

Additional symmetries of generalized integrable hierarchies

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