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.

scholarly journals Nonlinear Super Integrable Couplings of Super Classical-Boussinesq Hierarchy

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Xiuzhi Xing ◽  
Jingzhu Wu ◽  
Xianguo Geng
Keyword(s):  
Integrable Hierarchy ◽  
Trace Identity ◽  
Hamiltonian Structures ◽  
Integrable Couplings ◽  
Classical Integrable

Nonlinear integrable couplings of super classical-Boussinesq hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then, its super Hamiltonian structures were established by using super trace identity. As its reduction, nonlinear integrable couplings of the classical integrable hierarchy were obtained.

A NEW LOOP ALGEBRA AND TWO NEW LIOUVILLE INTEGRABLE HIERARCHY

2007 ◽  
Vol 21 (11) ◽  
pp. 663-673 ◽  
Author(s):  
HUAN-HE DONG
Keyword(s):  
Quadratic Form ◽  
Loop Algebra ◽  
Integrable Hierarchy ◽  
Trace Identity ◽  
Hamiltonian Structures ◽  
Liouville Integrable

A new loop algebra containing four arbitrary constants is presented, and the corresponding computing formula of constant γ in the quadratic-form identity is obtained in this paper, which can be reduced to a computing formula of constant γ in the trace identity. As application, two new Liouville integrable hierarchy and Hamiltonian structures are derived.

scholarly journals Two Expanding Integrable Models of the Geng-Cao Hierarchy

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Xiurong Guo ◽  
Yufeng Zhang ◽  
Xuping Zhang
Keyword(s):  
Heat Equation ◽  
Lie Algebras ◽  
Burgers Equation ◽  
Integrable Model ◽  
Integrable Models ◽  
Trace Identity ◽  
Hamiltonian Structures ◽  
Generalized Burgers Equation ◽  
Integrable Couplings ◽  
Integrable Coupling

As far as linear integrable couplings are concerned, one has obtained some rich and interesting results. In the paper, we will deduce two kinds of expanding integrable models of the Geng-Cao (GC) hierarchy by constructing different 6-dimensional Lie algebras. One expanding integrable model (actually, it is a nonlinear integrable coupling) reduces to a generalized Burgers equation and further reduces to the heat equation whose expanding nonlinear integrable model is generated. Another one is an expanding integrable model which is different from the first one. Finally, the Hamiltonian structures of the two expanding integrable models are obtained by employing the variational identity and the trace identity, respectively.

scholarly journals Bi-Integrable Couplings of a New Soliton Hierarchy Associated withSO(4)

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Yan Cao ◽  
Liangyun Chen ◽  
Baiying He
Keyword(s):  
Lie Algebra ◽  
Integrable Hierarchy ◽  
Hamiltonian Structures ◽  
Spectral Problems ◽  
Zero Curvature ◽  
Soliton Hierarchy ◽  
Integrable Couplings ◽  
Orthogonal Lie Algebra ◽  
Isospectral Problem

Based on the six-dimensional real special orthogonal Lie algebraSO(4), a new Lax integrable hierarchy is obtained by constructing an isospectral problem. Furthermore, we construct bi-integrable couplings for this hierarchy from the enlarged matrix spectral problems and the enlarged zero curvature equations. Hamiltonian structures of the obtained bi-integrable couplings are constructed by the variational identity.

scholarly journals A New Super Extension of Dirac Hierarchy

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Jiao Zhang ◽  
Fucai You ◽  
Yan Zhao
Keyword(s):  
Spectral Problem ◽  
Integrable Hierarchy ◽  
Trace Identity ◽  
Hamiltonian Structures ◽  
Curvature Equation ◽  
Zero Curvature

We derive a new super extension of the Dirac hierarchy associated with a3×3matrix super spectral problem with the help of the zero-curvature equation. Super trace identity is used to furnish the super Hamiltonian structures for the resulting nonlinear super integrable hierarchy.

A HIERARCHY OF HAMILTONIAN EQUATIONS ASSOCIATED WITH THE MODIFIED JAULENT–MIODEK HIERARCHY

2010 ◽  
Vol 24 (02) ◽  
pp. 183-193
Author(s):  
HAI-YONG DING ◽  
HONG-XIANG YANG ◽  
YE-PENG SUN ◽  
LI-LI ZHU
Keyword(s):  
Eigenvalue Problem ◽  
Evolution Equations ◽  
Trace Identity ◽  
Liouville Integrability ◽  
Matrix Eigenvalue Problem ◽  
Hamiltonian Structures ◽  
Hamiltonian Equations ◽  
Matrix Eigenvalue ◽  
Integrable Evolution

By considering a new four-by-four matrix eigenvalue problem, a hierarchy of Lax integrable evolution equations with four potentials is derived. The Hamiltonian structures of the resulting hierarchy are established by means of the generalized trace identity. The Liouville integrability for the hierarchy of the resulting Hamiltonian equations is presented.

A FOUR-BY-FOUR MATRIX EIGENVALUE PROBLEM, RELATED HIERARCHY OF LAX INTEGRABLE EQUATIONS AND THEIR HAMILTONIAN STRUCTURES

2008 ◽  
Vol 22 (23) ◽  
pp. 4027-4040 ◽  
Author(s):  
XI-XIANG XU ◽  
HONG-XIANG YANG ◽  
WEI-LI CAO
Keyword(s):  
Eigenvalue Problem ◽  
Evolution Equations ◽  
Trace Identity ◽  
Liouville Integrability ◽  
Matrix Eigenvalue Problem ◽  
Hamiltonian Structures ◽  
Hamiltonian Equations ◽  
Integrable Equations ◽  
Matrix Eigenvalue ◽  
Integrable Evolution

Starting from a new four-by-four matrix eigenvalue problem, a hierarchy of Lax integrable evolution equations with four potentials is derived. The Hamiltonian structures of the resulting hierarchy are established by means of the generalized trace identity. The Liouville integrability for the hierarchy of the resulting Hamiltonian equations is proved.

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