一族可积晶格孤子方程及其可积辛映射

A Hierarchy of Integrable Lattice Soliton Equations and Its Integrable Symplectic Map

得到一族对应于一类３×３矩阵离散谱问题的新的可积晶格孤子方程及其Ｈａｍｉｌｔｏｎ结构．方程族的Ｌａｘ对及其伴随Ｌａｘ对的非线性化得到１个可积辛映射．进而导出这族晶格方程的典型系统的解可化为常微分方程组的解和辛映射的简单迭化过程．

A hierarchy of integrable lattice soliton equations and its Hamiltonian structure associated with a 3×3 matrix spectral problem are got and an integrable symplectic map is obtained by nonlinearization of Lax pairs and adjoint Lax pairs of the hierarchy. Moreover, the solutions of the prototype system in the lattice equations hierarchy are reduced to the solutions of a system of ordinary differential equations and a simple iterative process of the symplectic map.