scholarly journals Nonlinear integrable couplings of a generalized super Ablowitz-Kaup-Newell-Segur hierarchy and its super bi-Hamiltonian structures

2017 ◽  
Vol 41 (4) ◽  
pp. 1565-1577 ◽  
Author(s):  
Beibei Hu ◽  
Wen-Xiu Ma ◽  
Tiecheng Xia ◽  
Ling Zhang
Keyword(s):  
Hamiltonian Structures ◽  
Integrable Couplings

scholarly journals Nonlinear Super Integrable Couplings of Super Broer-Kaup-Kupershmidt Hierarchy and Its Super Hamiltonian Structures

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Sixing Tao ◽  
Tiecheng Xia
Keyword(s):  
Poisson Bracket ◽  
Integrable Hierarchy ◽  
Trace Identity ◽  
Hamiltonian Structures ◽  
Integrable Couplings ◽  
Classical Integrable

Nonlinear integrable couplings of super Broer-Kaup-Kupershmidt hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then its super Hamiltonian structures were established by using super trace identity, and the conserved functionals were proved to be in involution in pairs under the defined Poisson bracket. As its reduction, nonlinear integrable couplings of the classical integrable hierarchy were obtained.

HAMILTONIAN STRUCTURES OF TWO INTEGRABLE COUPLINGS OF THE MODIFIED AKNS HIERARCHY

2007 ◽  
Vol 21 (30) ◽  
pp. 2063-2074 ◽  
Author(s):  
YUFENG ZHANG ◽  
Y. C. HON
Keyword(s):  
Lie Algebra ◽  
Hamiltonian Structure ◽  
Three Dimensional ◽  
Hamiltonian Structures ◽  
Akns Hierarchy ◽  
Higher Dimensional ◽  
Integrable Couplings

The extension of a three-dimensional Lie algebra into two higher-dimensional ones is used to deduce two new integrable couplings of the m-AKNS hierarchy. The Hamiltonian structures of the two integrable couplings are obtained, respectively. Specially, the complex Hamiltonian structure of the second integrable couplings is given.

Nonlinear bi-integrable couplings with Hamiltonian structures

2016 ◽  
Vol 127 ◽  
pp. 166-177 ◽  
Author(s):  
Wen-Xiu Ma ◽  
Jinghan Meng ◽  
Mengshu Zhang
Keyword(s):  
Hamiltonian Structures ◽  
Integrable Couplings

scholarly journals A novel kind of AKNS integrable couplings and their Hamiltonian structures

2017 ◽  
Vol 41 ◽  
pp. 1467-1476 ◽  
Author(s):  
Yu-Juan ZHANG ◽  
Wen-Xiu MA ◽  
Ömer ÜNSAL
Keyword(s):  
Hamiltonian Structures ◽  
Integrable Couplings

scholarly journals Bi-integrable and tri-integrable couplings of a soliton hierarchy associated with SO(4)

2017 ◽  
Vol 15 (1) ◽  
pp. 203-217
Author(s):  
Jian Zhang ◽  
Chiping Zhang ◽  
Yunan Cui
Keyword(s):  
Lie Algebra ◽  
Discrete Case ◽  
Hamiltonian Structures ◽  
Spectral Problems ◽  
Zero Curvature ◽  
Soliton Hierarchy ◽  
Integrable Couplings ◽  
Orthogonal Lie Algebra

Abstract In our paper, the theory of bi-integrable and tri-integrable couplings is generalized to the discrete case. First, based on the six-dimensional real special orthogonal Lie algebra SO(4), we construct bi-integrable and tri-integrable couplings associated with SO(4) for a hierarchy from the enlarged matrix spectral problems and the enlarged zero curvature equations. Moreover, Hamiltonian structures of the obtained bi-integrable and tri-integrable couplings are constructed by the variational identities.

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