Hamiltonian Forms for a Hierarchy of Discrete Integrable Coupling Systems

2008 ◽  
Vol 50 (6) ◽  
pp. 1269-1275 ◽  
Author(s):  
Xu Xi-Xiang ◽  
Yang Hong-Xiang ◽  
Lu Rong-Wu
Keyword(s):  
Hamiltonian Forms ◽  
Integrable Coupling

A FAMILY OF DISCRETE INTEGRABLE COUPLING SYSTEMS AND ITS LIOUVILLE INTEGRABILITY

2009 ◽  
Vol 23 (13) ◽  
pp. 1671-1685
Author(s):  
XI-XIANG XU ◽  
HONG-XIANG YANG
Keyword(s):  
Spectral Problem ◽  
Lie Algebras ◽  
Integrable Systems ◽  
Liouville Integrability ◽  
Discrete Integrable Systems ◽  
Direct Sum ◽  
The Family ◽  
Matrix Spectral Problem ◽  
Hamiltonian Forms ◽  
Integrable Coupling

A discrete matrix spectral problem and corresponding family of discrete integrable systems are discussed. A semi-direct sum of Lie algebras of four-by-four matrices is introduced, and the related integrable coupling systems of resulting discrete integrable systems are derived. The obtained discrete integrable coupling systems are all written in their Hamiltonian forms by the discrete variational identity. Finally, Liouville integrability of the family of obtained integrable coupling systems is demonstrated.

scholarly journals On (2+1)-dimensional expanding integrable model of the Davey-Stewartson hierarchy

2021 ◽  
Vol 25 (6 Part B) ◽  
pp. 4431-4439
Author(s):  
Xiu-Rong Guo ◽  
Fang-Fang Ma ◽  
Juan Wang
Keyword(s):  
Lie Algebras ◽  
Hamiltonian Structure ◽  
Integrable Model ◽  
Coupling System ◽  
Integrable Coupling ◽  
Type Abstraction Hierarchy

This paper mainly investigates the reductions of an integrable coupling of the Levi hierarchy and an expanding model of the (2+1)-dimensional Davey-Stewartson hierarchy. It is shown that the integrable coupling system of the Levi hierarchy possesses a quasi-Hamiltonian structure under certain constraints. Based on the Lie algebras construct, The type abstraction hierarchy scheme is used to gener?ate the (2+1)-dimensional expanding integrable model of the Davey-Stewartson hierarchy.

scholarly journals The Semidirect Sum of Lie Algebras and Its Applications to C-KdV Hierarchy

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Xia Dong ◽  
Tiecheng Xia ◽  
Desheng Li
Keyword(s):  
Quadratic Form ◽  
Lie Algebras ◽  
Integrable Systems ◽  
The Other ◽  
Loop Algebra ◽  
Hamiltonian Structures ◽  
Kdv Hierarchy ◽  
Integrable Coupling

By use of the loop algebraG-~, integrable coupling of C-KdV hierarchy and its bi-Hamiltonian structures are obtained by Tu scheme and the quadratic-form identity. The method can be used to produce the integrable coupling and its Hamiltonian structures to the other integrable systems.

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