An unified form of the AKNS and BPT hierarchies with two arbitrary parameters

Engui Fan; Honwah Tam; Yufeng Zhang

doi:10.1016/j.physleta.2006.07.059

An unified form of the AKNS and BPT hierarchies with two arbitrary parameters

Engui Fan^*
, Honwah Tam
, Yufeng Zhang

^*Corresponding author for this work

Department of Computer Science

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

3 Citations (Scopus)

Abstract

We present a new basis of the loop algebra over(A, ̃)₁ which is devote to setting up a new isospectral problem. By using Tu scheme, a new Liouville integrable hierarchy of soliton equations with two arbitrary parameters, which possesses the bi-Hamiltonian structure, is worked out. As reduction cases, it is shown that the hierarchy can be decomposed into the well-known AKNS hierarchy and the BPT hierarchy by taking different values of the parameters respectively. We call the hierarchy as an unified expression of the AKNS and the BPT hierarchies.

Original language	English
Pages (from-to)	99-104
Number of pages	6
Journal	Physics Letters A
Volume	360
Issue number	1
DOIs	https://doi.org/10.1016/j.physleta.2006.07.059
Publication status	Published - 18 Dec 2006

User-Defined Keywords

AKNS hierarchy
BPT hierarchy
Hamiltonian structure
Loop algebra

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10.1016/j.physleta.2006.07.059

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title = "An unified form of the AKNS and BPT hierarchies with two arbitrary parameters",

abstract = "We present a new basis of the loop algebra over(A,{\~ })1 which is devote to setting up a new isospectral problem. By using Tu scheme, a new Liouville integrable hierarchy of soliton equations with two arbitrary parameters, which possesses the bi-Hamiltonian structure, is worked out. As reduction cases, it is shown that the hierarchy can be decomposed into the well-known AKNS hierarchy and the BPT hierarchy by taking different values of the parameters respectively. We call the hierarchy as an unified expression of the AKNS and the BPT hierarchies.",

keywords = "AKNS hierarchy, BPT hierarchy, Hamiltonian structure, Loop algebra",

author = "Engui Fan and Honwah Tam and Yufeng Zhang",

note = "Funding Information: This work was supported by The National Science Foundations of China (10371023, 10471139), National Key Basic Research Project of China (2004CB318000) and Hong Kong Research Grant Council grant No. HKBU 2016/05p.",

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AU - Fan, Engui

AU - Tam, Honwah

AU - Zhang, Yufeng

N1 - Funding Information: This work was supported by The National Science Foundations of China (10371023, 10471139), National Key Basic Research Project of China (2004CB318000) and Hong Kong Research Grant Council grant No. HKBU 2016/05p.

PY - 2006/12/18

Y1 - 2006/12/18

N2 - We present a new basis of the loop algebra over(A, ̃)1 which is devote to setting up a new isospectral problem. By using Tu scheme, a new Liouville integrable hierarchy of soliton equations with two arbitrary parameters, which possesses the bi-Hamiltonian structure, is worked out. As reduction cases, it is shown that the hierarchy can be decomposed into the well-known AKNS hierarchy and the BPT hierarchy by taking different values of the parameters respectively. We call the hierarchy as an unified expression of the AKNS and the BPT hierarchies.

AB - We present a new basis of the loop algebra over(A, ̃)1 which is devote to setting up a new isospectral problem. By using Tu scheme, a new Liouville integrable hierarchy of soliton equations with two arbitrary parameters, which possesses the bi-Hamiltonian structure, is worked out. As reduction cases, it is shown that the hierarchy can be decomposed into the well-known AKNS hierarchy and the BPT hierarchy by taking different values of the parameters respectively. We call the hierarchy as an unified expression of the AKNS and the BPT hierarchies.

KW - AKNS hierarchy

KW - BPT hierarchy

KW - Hamiltonian structure

KW - Loop algebra

UR - https://www.scopus.com/pages/publications/33750294072

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DO - 10.1016/j.physleta.2006.07.059

M3 - Journal article

AN - SCOPUS:33750294072

SN - 0375-9601

VL - 360

SP - 99

EP - 104

JO - Physics Letters A

JF - Physics Letters A

IS - 1

ER -

An unified form of the AKNS and BPT hierarchies with two arbitrary parameters

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