The Liouville integrable coupling system of the m-AKNS hierarchy and its Hamiltonian structure

2007 ◽  
Vol 16 (3) ◽  
pp. 595-598 ◽  
Author(s):  
Yue Chao ◽  
Yang Geng-Wen ◽  
Xu Yue-Cai
Keyword(s):  
Hamiltonian Structure ◽  
Akns Hierarchy ◽  
Coupling System ◽  
Liouville Integrable ◽  
Integrable Coupling

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 A Hierarchy of Discrete Integrable Coupling System with Self-Consistent Sources

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Yuqing Li ◽  
Huanhe Dong ◽  
Baoshu Yin
Keyword(s):  
Quadratic Form ◽  
Hamiltonian Structure ◽  
Liouville Integrability ◽  
Soliton Equation ◽  
Coupling System ◽  
Self Consistent ◽  
Integrable Coupling

Integrable coupling system of a lattice soliton equation hierarchy is deduced. The Hamiltonian structure of the integrable coupling is constructed by using the discrete quadratic-form identity. The Liouville integrability of the integrable coupling is demonstrated. Finally, the discrete integrable coupling system with self-consistent sources is deduced.

scholarly journals A Complex Integrable Hierarchy and Its Hamiltonian Structure for Integrable Couplings of WKI Soliton Hierarchy

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Fajun Yu ◽  
Shuo Feng ◽  
Yanyu Zhao
Keyword(s):  
Hamiltonian Structure ◽  
Direct Application ◽  
Integrable Hierarchy ◽  
Soliton Equation ◽  
Zero Curvature ◽  
Coupling System ◽  
Soliton Hierarchy ◽  
Integrable Couplings ◽  
Nonlinear Composite ◽  
Integrable Coupling

We generate complex integrable couplings from zero curvature equations associated with matrix spectral problems in this paper. A direct application to the WKI spectral problem leads to a novel soliton equation hierarchy of integrable coupling system; then we consider the Hamiltonian structure of the integrable coupling system. We select theU¯,V¯and generate the nonlinear composite parts, which generate new extended WKI integrable couplings. It is also indicated that the method of block matrix is an efficient and straightforward way to construct the integrable coupling system.

A KIND OF NEW CONTINUOUS LIMITS OF AN INTEGRABLE COUPLING SYSTEM FOR DISCRETE AKNS HIERARCHY

2011 ◽  
Vol 25 (26) ◽  
pp. 3443-3454
Author(s):  
FA-JUN YU
Keyword(s):  
Spectral Problem ◽  
Lie Algebra ◽  
Continuous Limit ◽  
Soliton Equation ◽  
Akns Hierarchy ◽  
Complex Lattice ◽  
Coupling System ◽  
Integrable Couplings ◽  
Integrable Coupling

We present a kind of new continuous limits of an integrable coupling system for discrete AKNS hierarchy by using of Lie algebra sl(4). By introducing a complex discrete spectral problem, a coupling lattice hierarchy is derived. It is shown that a new sequence of combinations of complex lattice spectral problem converges to the integrable couplings of soliton equation hierarchy, which has the integrable coupling system of AKNS hierarchy as a continuous limit.

NEW INTEGRABLE LATTICE HIERARCHY AND ITS INTEGRABLE COUPLING

2009 ◽  
Vol 23 (23) ◽  
pp. 4791-4800 ◽  
Author(s):  
ZHU LI ◽  
HUANHE DONG
Keyword(s):  
Spectral Problem ◽  
Hamiltonian Structure ◽  
Lattice Equation ◽  
Integrable Lattice ◽  
Integrable Couplings ◽  
Liouville Integrable ◽  
Integrable Coupling

New hierarchy of Liouville integrable lattice equation and their Hamiltonian structure are generated by use of the Tu model. Then, integrable couplings of the obtained system is worked out by the extending spectral problem.

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