Two new discrete integrable systems

doi:10.1088/1674-1056/22/3/030203

中国物理B ›› 2013, Vol. 22 ›› Issue (3): 30203-030203.doi: 10.1088/1674-1056/22/3/030203

Two new discrete integrable systems

陈晓红^{a b}, 张鸿庆^a

a School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China;
b School of Science, University of Science and Technology Liaoning, Anshan 114051, China

收稿日期:2012-05-11 修回日期:2012-11-01 出版日期:2013-02-01 发布日期:2013-02-01

Two new discrete integrable systems

Chen Xiao-Hong (陈晓红)^{a b}, Zhang Hong-Qing (张鸿庆)^a

a School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China;
b School of Science, University of Science and Technology Liaoning, Anshan 114051, China

Received:2012-05-11 Revised:2012-11-01 Online:2013-02-01 Published:2013-02-01
Contact: Chen Xiao-Hong E-mail:xhchspring@163.com

摘要/Abstract

摘要： In this paper, we focus on the construction of new (1+1)-dimensional discrete integrable systems according to a subalgebra of loop algebra Â1. By designing two new (1+1)-dimensional discrete spectral problems, two new discrete integrable systems are obtained, namely, a 2-field lattice hierarchy and a 3-field lattice hierarchy. When deriving the two new discrete integrable systems, we find the generalized relativistic Toda lattice hierarchy and the generalized modified Toda lattice hierarchy. Moreover, we also obtain the Hamiltonian structures of the two lattice hierarchies by means of the discrete trace identity.

关键词: discrete integrable system, Hamiltonian structure, loop algebra

Abstract: In this paper, we focus on the construction of new (1+1)-dimensional discrete integrable systems according to a subalgebra of loop algebra Â1. By designing two new (1+1)-dimensional discrete spectral problems, two new discrete integrable systems are obtained, namely, a 2-field lattice hierarchy and a 3-field lattice hierarchy. When deriving the two new discrete integrable systems, we find the generalized relativistic Toda lattice hierarchy and the generalized modified Toda lattice hierarchy. Moreover, we also obtain the Hamiltonian structures of the two lattice hierarchies by means of the discrete trace identity.

Key words: discrete integrable system, Hamiltonian structure, loop algebra

中图分类号: (Integrable systems)

02.30.Ik

陈晓红, 张鸿庆. Two new discrete integrable systems[J]. 中国物理B, 2013, 22(3): 30203-030203.

Chen Xiao-Hong (陈晓红), Zhang Hong-Qing (张鸿庆). Two new discrete integrable systems[J]. Chin. Phys. B, 2013, 22(3): 30203-030203.

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Two new discrete integrable systems

Two new discrete integrable systems

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