A Centerless Virasoro Algebra of Master Symmetries for the Ablowitz-Ladik Hierarchy
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
A Centerless Virasoro Algebra of Master Symmetries for the Ablowitz-Ladik Hierarchy
|
|
| Creator |
Haine, L.
Vanderstichelen, D. |
|
| Description |
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].
|
|
| Date |
2019-02-21T07:26:52Z
2019-02-21T07:26:52Z 2013 |
|
| Type |
Article
|
|
| Identifier |
A Centerless Virasoro Algebra of Master Symmetries for the Ablowitz-Ladik Hierarchy / L. Haine, D. Vanderstichelen // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 39 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 37K10; 17B68 DOI: http://dx.doi.org/10.3842/SIGMA.2013.079 http://dspace.nbuv.gov.ua/handle/123456789/149371 |
|
| Language |
en
|
|
| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
|
|
| Publisher |
Інститут математики НАН України
|
|