Hamiltonian Structures of KdV-Type Hierarchies and Associated W-Algebras

Yi Cheng; Qing Chen; Jingsong He

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Hamiltonian Structures of KdV-Type Hierarchies and Associated W-Algebras

Yi Cheng·Qing Chen·Jingsong He

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Abstract

The $(n,m)^þ$ KdV hierarchy is a restriction of the KP hierarchy to a submanifold of pseudo-differential operators in a radio form. Explicit formula of the restricted Hamiltonian structure of KP is given which provides a new, more constructive proof of the isomorphism between the associated $W(n,m)$-algebra to $W_{n+m}\oplus W_m\oplus U(1)$ algebra, and the Hamiltonian property of the $(n,m)^þ$ KdV hierarchy as well as its Lax-Manakov triad representation. Similarly the Hamiltonian property for a version of modified $n^þ$ KdV and the isomorphism between $W_n$-algebra to $W_l\oplus W_m\oplus U(1)$ algebra are shown, where $l+m=n$. The role of U(1) current in both cases is also explained.

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BibTeX RIS

Yi Cheng, Qing Chen, Jingsong He. 2000-10-08. Hamiltonian Structures of KdV-Type Hierarchies and Associated W-Algebras. https://arxiv.org/abs/nlin/0010018

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