一族Liouville可积系及其3-Ham ilton结构

A family of Liouville integrable systems and their Ham iltonian structures

构造了loop代数A1的一个高阶子代数,设计了一个新的Lax对.利用屠格式获得了含8个位势的孤立子方程族;利用Gauteax导数直接验证了所得3个辛算子的线性组合仍为辛算子.因此该孤立族具有3-Hamilton结构,具有无穷多个对合的公共守恒密度,故Liouville可积.作为约化情形,得到了2个可积系,其中之一是著名的AKNS方程族.

A high order subalgebra of loop algebra _1 is constructed.It follows that a new Lax pair is established.By making use of Tu scheme,a soliton hierarchy of equations with 8 potentials is obtained.Using Gauteax derivatives directly verifies that a linear combination of 3 symplectic operators is still a symplectic operator.Hence,the soliton hierarchy is Liouville integrable,possessing 3-Hamiltonian structure and infinite common conserved dentities in involution.As reductive cases,two integrable systems are presented,one of them is the well-known AKNS hierarchy.