Abstract A direct way to construct integrable couplings for discrete systems is presented by use of two semi-direct sum Lie algebras. As their applications, the discrete integrable couplings associated with modified Korteweg--de Vries (m-KdV) lattice and two hierarchies of discrete soliton equations are developed. It is also indicated that the study of integrable couplings using semi-direct sums of Lie algebras is an important step towards the complete classification of integrable couplings.
Received: 08 August 2006
Revised: 18 December 2006
Accepted manuscript online:
Dong Huan-He(董焕河) Discrete integrable couplings associated with modified Korteweg--de Vries lattice and two hierarchies of discrete soliton equations 2007 Chinese Physics 16 1177
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