A few expanding Lie algebras of the Lie algebra A1 and applications

Yufeng Zhang; Engui Fan; Hon Wah TAM

doi:10.1016/j.physleta.2006.07.003

A few expanding Lie algebras of the Lie algebra A₁ and applications

Yufeng Zhang^*, Engui Fan, Hon Wah TAM

^*Corresponding author for this work

Department of Computer Science

Research output: Contribution to journal › Journal article › peer-review

28 Citations (Scopus)

Abstract

Based on two foundational subalgebras of the Lie algebra A₁, a few expanding higher-dimensional Lie algebras are presented to generate four integrable couplings of a soliton equation hierarchy. The Hamiltonian structure for one of them is obtained by using the quadratic-form identity. The classification of the Lie algebras is also given. Moreover, a decomposition of one higher-dimensional Lie algebra is demonstrated to produce a q-integrable expanding hierarchy for generalized q-form KdV hierarchy.

Original language	English
Pages (from-to)	471-480
Number of pages	10
Journal	Physics Letters A
Volume	359
Issue number	5
DOIs	https://doi.org/10.1016/j.physleta.2006.07.003
Publication status	Published - 4 Dec 2006

Scopus Subject Areas

Physics and Astronomy(all)

User-Defined Keywords

Integrable coupling
Lie algebra
Soliton equation

Access to Document

10.1016/j.physleta.2006.07.003

Cite this

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title = "A few expanding Lie algebras of the Lie algebra A1 and applications",

abstract = "Based on two foundational subalgebras of the Lie algebra A1, a few expanding higher-dimensional Lie algebras are presented to generate four integrable couplings of a soliton equation hierarchy. The Hamiltonian structure for one of them is obtained by using the quadratic-form identity. The classification of the Lie algebras is also given. Moreover, a decomposition of one higher-dimensional Lie algebra is demonstrated to produce a q-integrable expanding hierarchy for generalized q-form KdV hierarchy.",

keywords = "Integrable coupling, Lie algebra, Soliton equation",

author = "Yufeng Zhang and Engui Fan and TAM, {Hon Wah}",

note = "Funding Information: This work was supported by The National Science Foundations of China (10471139, 10371023), Shanghai Shuguang Project (02SG02) and Hong Kong Research Grant Council grant number HKBU 2016/05P. ",

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T1 - A few expanding Lie algebras of the Lie algebra A1 and applications

AU - Zhang, Yufeng

AU - Fan, Engui

AU - TAM, Hon Wah

N1 - Funding Information: This work was supported by The National Science Foundations of China (10471139, 10371023), Shanghai Shuguang Project (02SG02) and Hong Kong Research Grant Council grant number HKBU 2016/05P.

PY - 2006/12/4

Y1 - 2006/12/4

N2 - Based on two foundational subalgebras of the Lie algebra A1, a few expanding higher-dimensional Lie algebras are presented to generate four integrable couplings of a soliton equation hierarchy. The Hamiltonian structure for one of them is obtained by using the quadratic-form identity. The classification of the Lie algebras is also given. Moreover, a decomposition of one higher-dimensional Lie algebra is demonstrated to produce a q-integrable expanding hierarchy for generalized q-form KdV hierarchy.

AB - Based on two foundational subalgebras of the Lie algebra A1, a few expanding higher-dimensional Lie algebras are presented to generate four integrable couplings of a soliton equation hierarchy. The Hamiltonian structure for one of them is obtained by using the quadratic-form identity. The classification of the Lie algebras is also given. Moreover, a decomposition of one higher-dimensional Lie algebra is demonstrated to produce a q-integrable expanding hierarchy for generalized q-form KdV hierarchy.

KW - Integrable coupling

KW - Lie algebra

KW - Soliton equation

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