高阶HBK方程组的Lie对称分析,非线性自伴随和守恒律

摘要

By using Lie group analysis method to study the higher-order Broer-Kaup equations,the Lie point symmetries and an optimal system of HBK equations are obtained.And it is demonstrated that the HBK equations are nonlinear self-adjointness.This property is applied to construct infinitely many conservation laws of HBK equations with the corresponding Lie symmetry by Ibragimov thereom.%该文运用李群分析方法研究了高阶higer-order Broer-Kaup (HBK)方程组,求出了方程组的李点对称和一维最优系统.并证明了该方程组是非线性自伴随的,根据Ibragimov定理这个性质被用来构造了HBK方程组对称对应的无穷多守恒律.