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- W2168584573 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 Vel'azquez (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]." @default.
- W2168584573 created "2016-06-24" @default.
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- W2168584573 date "2013-12-12" @default.
- W2168584573 modified "2023-09-27" @default.
- W2168584573 title "A Centerless Virasoro Algebra of Master Symmetries for the Ablowitz-Ladik Hierarchy" @default.
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- W2168584573 doi "https://doi.org/10.3842/sigma.2013.079" @default.
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