Nonlinear bi-integrable couplings of a generalized Kaup–Newell type soliton hierarchy

Optik ◽  
2018 ◽  
Vol 172 ◽  
pp. 1003-1011 ◽  
Author(s):  
Xue Guan ◽  
Huiqun Zhang ◽  
Wenjun Liu
Keyword(s):  
Soliton Hierarchy ◽  
Integrable Couplings

INTEGRABLE COUPLINGS FOR THE ABLOWITZ–LADIK LATTICE THROUGH ENLARGING ASSOCIATED LAX PAIRS

2006 ◽  
Vol 20 (05) ◽  
pp. 253-259
Author(s):  
NING ZHANG ◽  
XI-XIANG XU ◽  
HONG-XIANG YANG
Keyword(s):  
Discrete Systems ◽  
Lax Pairs ◽  
Spectral Problems ◽  
Soliton Hierarchy ◽  
Integrable Couplings

A direct way to construct integrable couplings for discrete systems is introduced through enlarging associated spectral problems. As an application, the procedure for the Ablowitz–Ladik lattice soliton hierarchy is employed.

A SOLITON HIERARCHY FROM THE LEVI SPECTRAL PROBLEM AND ITS TWO INTEGRABLE COUPLINGS, HAMILTONIAN STRUCTURE

2009 ◽  
Vol 23 (05) ◽  
pp. 731-739
Author(s):  
YONGQING ZHANG ◽  
YAN LI
Keyword(s):  
Spectral Problem ◽  
Lie Algebras ◽  
Hamiltonian Structure ◽  
Soliton Equation ◽  
Curvature Equation ◽  
Loop Algebras ◽  
Zero Curvature ◽  
Soliton Hierarchy ◽  
Integrable Couplings ◽  
Time Part

A soliton-equation hierarchy from the D. Levi spectral problem is obtained under the framework of zero curvature equation. By employing two various multi-component Lie algebras and the loop algebras, we enlarge the Levi spectral problem and the corresponding time-part isospectral problems so that two different integrable couplings are produced. Using the quadratic-form identity yields the Hamiltonian structure of one of the two 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.

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 Bi-Integrable and Tri-Integrable Couplings of a Soliton Hierarchy Associated with SO(3)

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Jian Zhang ◽  
Chiping Zhang ◽  
Yunan Cui
Keyword(s):  
Lie Algebra ◽  
Three Dimensional ◽  
Hamiltonian Structures ◽  
Spectral Problems ◽  
Curvature Equation ◽  
Zero Curvature ◽  
Soliton Hierarchy ◽  
Integrable Couplings ◽  
Orthogonal Lie Algebra

Based on the three-dimensional real special orthogonal Lie algebra SO(3), by zero curvature equation, we present bi-integrable and tri-integrable couplings associated with SO(3) 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 applying the variational identities.

scholarly journals Self-Consistent Sources and Conservation Laws for Nonlinear Integrable Couplings of the Li Soliton Hierarchy

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Han-yu Wei ◽  
Tie-cheng Xia
Keyword(s):  
Conservation Laws ◽  
Lie Algebras ◽  
Soliton Hierarchy ◽  
Self Consistent ◽  
Integrable Couplings ◽  
Integrable Coupling

New explicit Lie algebras are introduced for which the nonlinear integrable couplings of the Li soliton hierarchy are obtained. Then, the nonlinear integrable couplings of Li soliton hierarchy with self-consistent sources are established. Finally, we present the infinitely many conservation laws for the nonlinear integrable coupling of Li soliton hierarchy.

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