Integrable semi-discretizations and full-discretization of the two-dimensional Leznov lattice

Abstract

In this paper, semi-discretizations and full-discretization of the Leznov lattice are investigated via Hirota's bilinear formalism. As a result, two integrable semi-discrete versions and one fully discrete version for the Leznov lattice are found. Bäcklund transformations, nonlinear superposition formulae and Lax pairs for these discrete versions are presented.

Mathematics Subject Classification (2000):

• 35Q58
• 37K40

Keywords:

• integrable system
• integrable discretization
• Bäcklund transformation
• Lax pair

Acknowledgements

The authors would like to thank the referee for valuable comments. This work was supported by the National Natural Science Foundation of China (Grant No. 10771207), the knowledge innovation programme of the Institute of Computational Math., AMSS and State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences.