An integrable coupling family of Merola–Ragnisco–Tu lattice systems, its Hamiltonian structure and related nonisospectral integrable lattice family

2010 ◽  
Vol 374 (3) ◽  
pp. 401-410 ◽  
Author(s):  
Xi-Xiang Xu
Keyword(s):  
Hamiltonian Structure ◽  
Lattice Systems ◽  
Integrable Lattice ◽  
Integrable Coupling

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.

scholarly journals Mastersymmetries and Multi-Hamiltonian Formulations for Some Integrable Lattice Systems

1989 ◽  
Vol 81 (2) ◽  
pp. 294-308 ◽  
Author(s):  
W. Oevel ◽  
H. Zhang ◽  
B. Fuchssteiner
Keyword(s):  
Lattice Systems ◽  
Integrable Lattice

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.

A generalized integrable hierarchy related to the relativistic Toda lattice: Hamiltonian structure, Darboux transformation, soliton solution and conservation law

2021 ◽  
Author(s):  
Zhiguo Xu
Keyword(s):  
Darboux Transformation ◽  
Hamiltonian Structure ◽  
Toda Lattice ◽  
Soliton Solutions ◽  
Integrable Hierarchy ◽  
Integrable Lattice ◽  
Pass Through ◽  
Matrix Spectral Problem ◽  
Relativistic Toda Lattice ◽  
Toda Lattice Hierarchy

Starting from a more generalized discrete [Formula: see text] matrix spectral problem and using the Tu scheme, some integrable lattice hierarchies (ILHs) are presented which include the well-known relativistic Toda lattice hierarchy and some new three-field ILHs. Taking one of the hierarchies as example, the corresponding Hamiltonian structure is constructed and the Liouville integrability is illustrated. For the first nontrivial lattice equation in the hierarchy, the [Formula: see text]-fold Darboux transformation (DT) of the system is established basing on its Lax pair. By using the obtained DT, we generate the discrete [Formula: see text]-soliton solutions in determinant form and plot their figures with proper parameters, from which we get some interesting soliton structures such as kink and anti-bell-shaped two-soliton, kink and anti-kink-shaped two-soliton and so on. These soliton solutions are much stable during the propagation, the solitary waves pass through without change of shapes, amplitudes, wave-lengths and directions. Finally, we derive infinitely many conservation laws of the system and give the corresponding conserved density and associated flux formulaically.

A solitary hierarchy of an integrable coupling and its Hamiltonian structure☆

2007 ◽  
Vol 34 (3) ◽  
pp. 914-918 ◽  
Author(s):  
Yu-Feng Zhang ◽  
Si-Hong Nian ◽  
En-Gui Fan
Keyword(s):  
Hamiltonian Structure ◽  
Integrable Coupling

THE INTEGRABLE PROPERTY OF LOTKA–VOLTERRA TYPE DISCRETE NONLINEAR LATTICE SOLITON SYSTEMS

2008 ◽  
Vol 22 (21) ◽  
pp. 2007-2019 ◽  
Author(s):  
XIN-YUE LI ◽  
XI-XIANG XU ◽  
QIU-LAN ZHAO
Keyword(s):  
Conservation Laws ◽  
Algebraic System ◽  
Hamiltonian Structure ◽  
Volterra Type ◽  
Soliton Equation ◽  
Nonlinear Lattice ◽  
Integrable Coupling

A hierarchy of discrete lattice soliton equation is obtained by using a novel algebraic system, and its Hamiltonian structure is generated by use of the Tu model. Then, conservation laws and integrable coupling of the obtained equation hierarchies are discussed.

scholarly journals Generalized integrable lattice systems

1992 ◽  
Vol 279 (3-4) ◽  
pp. 341-346 ◽  
Author(s):  
C.S. Xiong
Keyword(s):  
Lattice Systems ◽  
Integrable Lattice
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