中国物理B ›› 2007, Vol. 16 ›› Issue (5): 1177-1181.doi: 10.1088/1009-1963/16/5/001

• GENERAL •    下一篇

Discrete integrable couplings associated with modified Korteweg--de Vries lattice and two hierarchies of discrete soliton equations

董焕河   

  1. College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266510, China
  • 收稿日期:2006-08-08 修回日期:2006-12-18 出版日期:2007-05-20 发布日期:2007-05-20

Discrete integrable couplings associated with modified Korteweg--de Vries lattice and two hierarchies of discrete soliton equations

Dong Huan-He(董焕河)†   

  1. College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266510, China
  • Received:2006-08-08 Revised:2006-12-18 Online:2007-05-20 Published:2007-05-20

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摘要： 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.

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.

Key words: discrete integrable system, m-KdV lattice equation, semi-direct sums of Lie algebras

中图分类号:  (Integrable systems)

  • 02.30.Ik
02.10.Ud (Linear algebra) 05.45.Yv (Solitons)