Generalized Toda Mechanics Associated with Classical Lie Algebras D<SUB>r</SUB>

LIU Wang-Yun; YANG Zhan-Ying; ZHAO Liu

Chinese Physics C> 2004, Vol. 28> Issue(4) : 359-364

Generalized Toda Mechanics Associated with Classical Lie Algebras D_r

Institute of Modern Physics,Northwest University,Xi'an 710069,Chain

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In this paper, we construct the Lax pair of classical Lie algebra D_r according to the characteristic of its root system, and get a family of integrable generalizations of Toda mechanics (labeled by a pair of ordered integers (m,n), m,n denote the order of positive and negative roots respectively). We aiso provide the explicit equations of motion, the Hamiltonian and the Poission brackets corresponding to the case of m,n≤3.

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LIU Wang-Yun, YANG Zhan-Ying and ZHAO Liu. Generalized Toda Mechanics Associated with Classical Lie Algebras D_r[J]. Chinese Physics C, 2004, 28(4): 359-364.

LIU Wang-Yun, YANG Zhan-Ying and ZHAO Liu. Generalized Toda Mechanics Associated with Classical Lie Algebras D_r[J]. Chinese Physics C, 2004, 28(4): 359-364. shu

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Received: 2003-06-25
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

Generalized Toda Mechanics Associated with Classical Lie Algebras D_r

Corresponding author: LIU Wang-Yun,

Institute of Modern Physics,Northwest University,Xi'an 710069,Chain

Received Date: 2003-06-25

Accepted Date: 1900-01-01

Available Online: 2004-04-05

Abstract: In this paper, we construct the Lax pair of classical Lie algebra D_r according to the characteristic of its root system, and get a family of integrable generalizations of Toda mechanics (labeled by a pair of ordered integers (m,n), m,n denote the order of positive and negative roots respectively). We aiso provide the explicit equations of motion, the Hamiltonian and the Poission brackets corresponding to the case of m,n≤3.

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Generalized Toda Mechanics Associated with Classical Lie Algebras D_r

Generalized Toda Mechanics Associated with Classical Lie Algebras D_r