A Liouville integrable lattice soliton equation, infinitely many conservation laws and integrable coupling systems

2006 ◽  
Vol 349 (1-4) ◽  
pp. 153-163 ◽  
Author(s):  
Xi-Xiang Xu ◽  
Hong-Xiang Yang ◽  
Hai-Yong Ding
Keyword(s):  
Conservation Laws ◽  
Soliton Equation ◽  
Integrable Lattice ◽  
Liouville Integrable ◽  
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.

A HIERARCHY OF LIOUVILLE INTEGRABLE LATTICE EQUATION ASSOCIATED WITH A THREE-BY-THREE DISCRETE SPECTRAL PROBLEM AND ITS INFINITELY MANY CONSERVATION LAWS

2011 ◽  
Vol 25 (18) ◽  
pp. 2481-2492
Author(s):  
YU-QING LI ◽  
XI-XIANG XU
Keyword(s):  
Conservation Laws ◽  
Spectral Problem ◽  
Trace Identity ◽  
Lattice Equation ◽  
Hamiltonian Structures ◽  
Discrete Soliton ◽  
Soliton Equations ◽  
Integrable Lattice ◽  
Matrix Spectral Problem ◽  
Liouville Integrable

A discrete three-by-three matrix spectral problem is put forward and the corresponding discrete soliton equations are deduced. By means of the trace identity the Hamiltonian structures of the resulting equations are constructed, and furthermore, infinitely many conservation laws of the corresponding lattice system are obtained by a direct way.

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.

Notes on “infinite number of conservation laws and Darboux transformations for a 6-field integrable lattice system [Int. J. Mod. Phys. B 33 (2019) 1950147]

2021 ◽  
pp. 2150141
Author(s):  
Ning Zhang ◽  
Xi-Xiang Xu
Keyword(s):  
Conservation Laws ◽  
Darboux Transformation ◽  
Infinite Number ◽  
Lattice System ◽  
Darboux Transformations ◽  
Integrable Lattice

We show that the Darboux transformation in “Infinite number of conservation laws and Darboux transformations for a 6-field integrable lattice system” [Int. J. Mod. Phys. B 33 (2019) 1950147] is incorrect, and construct a correct Darboux transformation.

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