A new integrable symplectic map of Neumann type

Yongtang Wu*, Xianguo Geng

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

22 Citations (Scopus)


The nonlinearization approach is generalized to the case of the Neumann constraint associated with a discrete 3 × 3 matrix eigenvalue problem. A new symplectic map of the Neumann type is obtained by nonlinearization of the discrete eigenvalue problem and its adjoint one. A scheme for generating the involutive system of conserved integrals of the symplectic map is proposed, by which the symplectic map of the Neumann type is further proved to completely integrable. As an application, the calculation of solutions for the hierarchy of lattice soliton equations connected to the discrete eigenvalue problem is reduced to the solutions of a system of ordinary differential equations plus a simple iterative process of the symplectic map of the Neumann type.

Original languageEnglish
Pages (from-to)784-790
Number of pages7
JournalJournal of the Physical Society of Japan
Issue number3
Publication statusPublished - 15 Mar 1999
Externally publishedYes

Scopus Subject Areas

  • Physics and Astronomy(all)

User-Defined Keywords

  • Integrability
  • Lattice soliton equations
  • Symplectic map


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