r-matrix and algebraic-geometric symplectic map  

r-matrix and algebraic-geometric solution for integrable symplectic map

作　　者：QIAO ZhijunInstitute of Mathematics and School of Mathematical Sciences, Peking University, Beijing 100871, China 

出　　处：《Chinese Science Bulletin》1999年第2期114-118,共5页

摘　　要：A new Lax matrix is introduced for the integrable symplectic map (ISM), and the non-dynamical(i. e. constant) r-matrix of ISM is obtained. Moreover, an effective approach is systematically presented to construct the explicit solution(here, the explicit solution means algebraic-geometric solution expressed by the Riemann-Theta function) of a soliton system or nonlinear evolution equation from Lax matrix, r-matrix, and the theory of nonlinearization through taking the Toda lattice as an example. The given algebraic-geometric solution of the Toda lattice is almost-periodic and includes the periodic and finite-band solution.A new Lax matrix is introduced for the integrable symplectic map (ISM), and the non-dynamical (i.e. constant) r-matrix of ISM is obtained. Moreover, an effective approach is systematically presented to construct the explicit solution (here, the explicit solution means algebraic-geometric solution expressed by the Riemann-Theta function) of a soliton system or nonlinear evolution equation from Lax matrix, r-matrix, and the theory of nonlinearization through taking the Toda lattice as an example. The given algebraic-geometric solution of the Toda lattice is almost-periodic and includes the periodic and finite-band solution.

关 键 词：SYMPLECTIC MAP R-MATRIX algebraic-geometric solution. 

分 类 号：O187[理学—数学]