Non-isospectral integrable couplings of Ablowitz–Kaup–Newell–Segur (AKNS) hierarchy with self-consistent sources

2008 ◽  
Vol 17 (11) ◽  
pp. 3965-3973 ◽  
Author(s):  
Yu Fa-Jun ◽  
Li Li
Keyword(s):  
Akns Hierarchy ◽  
Self Consistent ◽  
Integrable Couplings

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.

Integrable couplings of a generalized AKNS hierarchy

2002 ◽  
Vol 9 (3) ◽  
pp. 220-223 ◽  
Author(s):  
Yu-feng Zhang ◽  
Hong-qing Zhang ◽  
Qing-you Yan
Keyword(s):  
Akns Hierarchy ◽  
Integrable Couplings

SPECTRAL RADIUS ANALYSIS OF MATRICES AND THE ASSOCIATED WITH INTEGRABLE SYSTEMS

2009 ◽  
Vol 23 (24) ◽  
pp. 4855-4879 ◽  
Author(s):  
HONWAH TAM ◽  
YUFENG ZHANG
Keyword(s):  
Lie Algebra ◽  
Spectral Radius ◽  
Integrable Systems ◽  
Hamiltonian Structure ◽  
Soliton Equation ◽  
Spectral Matrix ◽  
Akns Hierarchy ◽  
Integrable Couplings ◽  
Isospectral Problem ◽  
Set Up

An isospectral problem is introduced, a spectral radius of the corresponding spectral matrix is obtained, which enlightens us to set up an isospectral problem whose compatibility condition gives rise to a zero curvature equation in formalism, from which a Lax integrable soliton equation hierarchy with constraints of potential functions is generated along with 5 parameters, whose reduced cases present three integrable systems, i.e., AKNS hierarchy, Levi hierarchy and D-AKNS hierarchy. Enlarging the above Lie algebra into two bigger ones, the two integrable couplings of the hierarchy are derived, one of them has Hamiltonian structure by employing the quadratic-form identity or variational identity. The corresponding integrable couplings of the reduced systems are obtained, respectively. Finally, as comparing study for generating expanding integrable systems, a Lie algebra of antisymmetric matrices and its corresponding loop algebra are constructed, from which a great number of enlarging integrable systems could be generated, especially their Hamiltonian structure could be computed by the trace identity.

KN EQUATIONS HIERARCHY WITH SELF-CONSISTENT SOURCES AND ITS INTEGRABLE COUPLINGS

2011 ◽  
Vol 25 (25) ◽  
pp. 3325-3335
Author(s):  
FA-JUN YU ◽  
JIN-CAI CHANG
Keyword(s):  
Lie Algebra ◽  
Kronecker Product ◽  
Loop Algebra ◽  
Soliton Hierarchy ◽  
Self Consistent ◽  
Integrable Couplings

A hierarchy of the KN equations with self-consistent sources is derived with the Lie algebra sl(4). As an application example, the integrable couplings of the KN soliton hierarchy with self-consistent sources are constructed by using of Kronecker product and loop algebra [Formula: see text].

scholarly journals Nonlinear Bi-Integrable Couplings of Multicomponent Guo Hierarchy with Self-Consistent Sources

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Hongwei Yang ◽  
Huanhe Dong ◽  
Baoshu Yin ◽  
Zhenyu Liu
Keyword(s):  
Lie Algebra ◽  
Semisimple Lie Algebra ◽  
Hamiltonian Structures ◽  
Self Consistent ◽  
Integrable Couplings

Based on a well-known Lie algebra, the multicomponent Guo hierarchy with self-consistent sources is proposed. With the help of a set of non-semisimple Lie algebra, the nonlinear bi-integrable couplings of the multicomponent Guo hierarchy with self-consistent sources are obtained. It enriches the content of the integrable couplings of hierarchies with self-consistent sources. Finally, the Hamiltonian structures are worked out by employing the variational identity.

scholarly journals THE TRANSFORMATION BETWEEN THE AKNS HIERARCHY AND THE KN HIERARCHY WITH SELF-CONSISTENT SOURCES

2011 ◽  
Vol 18 (4) ◽  
pp. 483-490
Author(s):  
QI LI ◽  
WEN ZHANG ◽  
QIU-YUAN DUAN ◽  
DENG-YUAN CHEN
Keyword(s):  
Akns Hierarchy ◽  
Self Consistent
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