A generalized SHGI integrable hierarchy and its expanding integrable model

doi:10.1088/1009-1963/13/3/008

中国物理B ›› 2004, Vol. 13 ›› Issue (3): 307-311.doi: 10.1088/1009-1963/13/3/008

A generalized SHGI integrable hierarchy and its expanding integrable model

张玉峰

Institute of Mathematics, Information School, Shandong University of Sciences and Technology, Taian 271019, China

收稿日期:2003-04-22 修回日期:2003-09-03 出版日期:2004-03-06 发布日期:2005-07-06

A generalized SHGI integrable hierarchy and its expanding integrable model

Zhang Yu-Feng (张玉峰)

Institute of Mathematics, Information School, Shandong University of Sciences and Technology, Taian 271019, China

Received:2003-04-22 Revised:2003-09-03 Online:2004-03-06 Published:2005-07-06

摘要/Abstract

摘要： An anti-symmetric loop algebra \overline{A}_2 is constructed. It follows that an integrable system is obtained by use of Tu's scheme. The eminent feature of this integrable system is that it is reduced to a generalized Schr?dinger equation, the well-known heat-conduction equation and a Gerdjkov－Ivanov (GI) equation. Therefore, we call it a generalized SHGI hierarchy. Next, a new high-dimensional subalgebra \tilde{G} of the loop algebra ?_2 is constructed. As its application, a new expanding integrable system with six potential functions is engendered.

关键词: integrable system, Hamiltonian structure, loop algebra

Abstract: An anti-symmetric loop algebra $\overline{A}_2$ is constructed. It follows that an integrable system is obtained by use of Tu's scheme. The eminent feature of this integrable system is that it is reduced to a generalized Schr?dinger equation, the well-known heat-conduction equation and a Gerdjkov－Ivanov (GI) equation. Therefore, we call it a generalized SHGI hierarchy. Next, a new high-dimensional subalgebra $\tilde{G}$ of the loop algebra $\tilde{A}_2$ is constructed. As its application, a new expanding integrable system with six potential functions is engendered.

Key words: integrable system, Hamiltonian structure, loop algebra

中图分类号: (Solutions of wave equations: bound states)

03.65.Ge

02.10.-v (Logic, set theory, and algebra)

张玉峰. A generalized SHGI integrable hierarchy and its expanding integrable model[J]. 中国物理B, 2004, 13(3): 307-311.

Zhang Yu-Feng (张玉峰). A generalized SHGI integrable hierarchy and its expanding integrable model[J]. Chinese Physics, 2004, 13(3): 307-311.

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A generalized SHGI integrable hierarchy and its expanding integrable model

A generalized SHGI integrable hierarchy and its expanding integrable model

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