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Symmetry, Integrability and Geometry: Methods and Applications, 2013, Volume 9, 079, 42 pp.
DOI: https://doi.org/10.3842/SIGMA.2013.079
(Mi sigma862)
 

This article is cited in 1 scientific paper (total in 1 paper)

A Centerless Virasoro Algebra of Master Symmetries for the Ablowitz–Ladik Hierarchy

Luc Haine, Didier Vanderstichelen

Institut de Recherche en Mathématique et Physique, Université catholique de Louvain, Chemin du Cyclotron 2, 1348 Louvain-la-Neuve, Belgium
Full-text PDF (588 kB) Citations (1)
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Abstract: We show that the (semi-infinite) Ablowitz–Ladik (AL) hierarchy admits a centerless Virasoro algebra of master symmetries in the sense of Fuchssteiner [Progr. Theoret. Phys. 70 (1983), 1508–1522]. An explicit expression for these symmetries is given in terms of a slight generalization of the Cantero, Moral and Velázquez (CMV) matrices [Linear Algebra Appl. 362 (2003), 29–56] and their action on the tau-functions of the hierarchy is described. The use of the CMV matrices turns out to be crucial for obtaining a Lax pair representation of the master symmetries. The AL hierarchy seems to be the first example of an integrable hierarchy which admits a full centerless Virasoro algebra of master symmetries, in contrast with the Toda lattice and Korteweg–de Vries hierarchies which possess only “half of” a Virasoro algebra of master symmetries, as explained in Adler and van Moerbeke [Duke Math. J. 80 (1995), 863–911], Damianou [Lett. Math. Phys. 20 (1990), 101–112] and Magri and Zubelli [Comm. Math. Phys. 141 (1991), 329–351].
Keywords: Ablowitz–Ladik hierarchy; master symmetries; Virasoro algebra.
Received: July 31, 2013; in final form November 30, 2013; Published online December 12, 2013
Bibliographic databases:
Document Type: Article
MSC: 37K10; 17B68
Language: English
Citation: Luc Haine, Didier Vanderstichelen, “A Centerless Virasoro Algebra of Master Symmetries for the Ablowitz–Ladik Hierarchy”, SIGMA, 9 (2013), 079, 42 pp.
Citation in format AMSBIB
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\by Luc~Haine, Didier~Vanderstichelen
\paper A Centerless Virasoro Algebra of Master Symmetries for the Ablowitz--Ladik Hierarchy
\jour SIGMA
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\vol 9
\papernumber 079
\totalpages 42
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Symmetry, Integrability and Geometry: Methods and Applications
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