修正的Boussinesq方程组的李对称分析、非线性自伴随及守恒律（英文）

Lie Symmetry Analysis, Nonlinear Self-Adjointness and Conservation Laws of Modified Boussinesq System

本文证明修正的Boussinesq方程组是非线性自伴随的,这个性质为利用Ibragimov定理求解方程组的守恒律提供了先决条件.利用经典李群法求出方程组的李点对称,最优系统.最后,利用Ibragimov定理求出方程组的李对称对应的无穷多非平凡守恒律.

The paper first proves the modified Boussinesq system is nonlinear self- adjointness, which provides the prerequisite for using Ibragimov theorem to obtain conservation laws for the system. By using the classical Lie group method, the Lie point symmetry and an optimal system of the system are derived. As a consequence, infinite nontrivial conservation laws of the system are obtained with the corresponding Lie point symmetry by Ibragimov theorem.