Acta mathematica scientia,Series A ›› 2017, Vol. 37 ›› Issue (5): 814-824.

Previous Articles     Next Articles

A New Integrable Nonlinear Lattice Equation Hierarchy and Their Integrable Symplectic Map

Zhang Ning1,2, Xia Tiecheng1   

  1. 1. Department of Mathematics, Shanghai University, Shanghai 200444;
    2. Department of Basical Courses, Shandong University of Science and Technology, Shandong Taian 271019
  • Received:2016-12-07 Revised:2017-04-21 Online:2017-10-26 Published:2017-10-26
  • Supported by:
    Supported by the NSFC (11271008, 61072147) and the Project of Shandong Province Higher Educational Science and Technology Program (J14LI58)

Abstract: In this paper, a discrete matrix spectral problem is introduced and a hierarchy of discrete integrable systems is derived. Their Hamiltonian structures are established, and it is shown that the resulting discrete systems are all Liouville integrable. Through binary nonlinearization method, the Bargmann symmetry constraint and a family of finite-dimension completely integrable systems are obtained. Finally, the representation of solutions for the discrete integrable systems are given.

Key words: Discrete integrable system, Hamiltonian structure, Liouville integrability, Bargmann symmetry constraint

CLC Number: 

  • O175
Trendmd