Abstract
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 language | English |
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Pages (from-to) | 784-790 |
Number of pages | 7 |
Journal | Journal of the Physical Society of Japan |
Volume | 68 |
Issue number | 3 |
DOIs | |
Publication status | Published - 15 Mar 1999 |
Externally published | Yes |
Scopus Subject Areas
- General Physics and Astronomy
User-Defined Keywords
- Integrability
- Lattice soliton equations
- Symplectic map