一族新的Lax可积格方程和它的积耦合体系

A new hierarchy of Lax integrable lattice equations and its integrable couplings system

首先利用环代数A^1和微分算子构建一种新的代数系统X。其次,利用这种代数系统提出了一个新的等谱问题,由离散的零曲率方程得到Lax可积的立方V o lterra格方程族。最后,通过扩展代数系统X得出了立方V o lterra格方程族的可积耦合体系。这种方法也能被应用到其它的格方程族中。

A new algebraic system X is constructed by using the known loop algebra ^~A1 and difference operators. Then a new isospectral problem is established by taking advantage of X. As a result a new I.ax integrable lattice hierarchy is obtained. Furthermore, by constructing an expanding algebraic system ^~X ,the integrable couplings system of the Cubic Voherra lattice hierarchy is worked out. The method can also be applied to other lattice equation hierarchies.