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.

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.

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 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 Direct linearization approach to discrete integrable systems associated with ℤ 𝒩 graded Lax pairs

2020 ◽  
Vol 476 (2237) ◽  
pp. 20200036
Author(s):  
Wei Fu
Keyword(s):  
Difference Equations ◽  
Bilinear Form ◽  
Integrable Systems ◽  
Solution Structure ◽  
Discrete Systems ◽  
Lax Pairs ◽  
Discrete Integrable Systems ◽  
Direct Linearization ◽  
Linear Integral ◽  
Linear Integral Equations

Fordy and Xenitidis [ J. Phys. A: Math. Theor. 50 (2017) 165205. ( doi:10.1088/1751-8121/aa639a )] recently proposed a large class of discrete integrable systems which include a number of novel integrable difference equations, from the perspective of Z N graded Lax pairs, without providing solutions. In this paper, we establish the link between the Fordy–Xenitidis (FX) discrete systems in coprime case and linear integral equations in certain form, which reveals solution structure of these equations. The bilinear form of the FX integrable difference equations is also presented together with the associated general tau function. Furthermore, the solution structure explains the connections between the FX novel models and the discrete Gel’fand–Dikii hierarchy.

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 Binary non-linearization of Lax pairs of Kaup-Newell soliton hierarchy

1996 ◽  
Vol 111 (9) ◽  
pp. 1135-1149 ◽  
Author(s):  
W. -X. Ma ◽  
Q. Ding ◽  
W. G. Zhang ◽  
B. Q. Lu
Keyword(s):  
Lax Pairs ◽  
Soliton Hierarchy
Sign in / Sign up

Export Citation Format

Share Document