Discrete integrable couplings associated with Toda-type lattice and two hierarchies of discrete soliton equations

2006 ◽  
Vol 357 (6) ◽  
pp. 454-461 ◽  
Author(s):  
Yufeng Zhang ◽  
Engui Fan ◽  
Yongqing Zhang
Keyword(s):  
Discrete Soliton ◽  
Soliton Equations ◽  
Integrable Couplings ◽  
Type Lattice

Method for Generating Discrete Soliton Equations. V

1983 ◽  
Vol 52 (3) ◽  
pp. 766-771 ◽  
Author(s):  
Eturo Date ◽  
Michio Jimbo ◽  
Tetsuji Miwa
Keyword(s):  
Discrete Soliton ◽  
Soliton Equations

On discrete soliton equations related to cellular automata

1995 ◽  
Vol 209 (3-4) ◽  
pp. 184-188 ◽  
Author(s):  
Daisuke Takahashi ◽  
Junta Matsukidaira
Keyword(s):  
Cellular Automata ◽  
Discrete Soliton ◽  
Soliton Equations

INTEGRABLE COUPLING SYSTEMS OF HAMILTONIAN LATTICE EQUATIONS BY SEMI-DIRECT SUMS OF LIE ALGEBRAS

2010 ◽  
Vol 24 (07) ◽  
pp. 681-694
Author(s):  
LI-LI ZHU ◽  
JUN DU ◽  
XIAO-YAN MA ◽  
SHENG-JU SANG
Keyword(s):  
Eigenvalue Problem ◽  
Lie Algebras ◽  
Hamiltonian Structure ◽  
Liouville Integrability ◽  
Direct Sums ◽  
Direct Sum ◽  
Hamiltonian Lattice ◽  
Integrable Couplings ◽  
Type Lattice ◽  
Integrable Coupling

By considering a discrete isospectral eigenvalue problem, a hierarchy of lattice soliton equations are derived. The relation to the Toda type lattice is achieved by variable transformation. With the help of Tu scheme, the Hamiltonian structure of the resulting lattice hierarchy is constructed. The Liouville integrability is then demonstrated. Semi-direct sum of Lie algebras is proposed to construct discrete integrable couplings. As applications, two kinds of discrete integrable couplings of the resulting system are worked out.

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.

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