Gerdjikov-Ivanon(GI)方程族与其一类扩展可积系统

Gerdjikov-Ivanon(GI) Equation Hierarchy and Its Type of Expanding Integrable System

利用loop代数A1的一个子代数,设计了两个等谱问题,利用其相容性条件,即零曲率方程,等价地导出了GI方程族.利用A1的子代数的一类已知扩展loop代数,设计Lax对,由此导出了GI方程族的一类扩展可积模型.

By using of a subalgebra of the loop algebra A1^-, two isospectral problems are established, whose compatibility condition, i. e. zero curvature equation, equivalently derive GI hierarchy. By taking use of the known expanding loop algerbra of the subalgerbra of A1^-, an isospectral Lax pair is given for which a kind of expanding integerable model of the GI hierarchy is worked out.