耦合Burgers方程的对称性及对称约化

对称性分析是自然科学研究中的重要方法之一. 利用对称性分析研究了一个描述两层流体体系的模型即耦合Burgers方程的对称性. 利用对称性给出了这个模型的四种对称性约化并给出了这些约化方程的一些特殊的严格解,如有理解、行波孤立子解和非行波孤立子解. 关键词： 对称性约化 耦合Burgers方程 孤立子

Symmetries and symmetry reductions of the coupled Burgers equation

Symmetry analysis is an important method used in almost all fields of natural science. In this paper, by means of the symmetry analysis, a new model, namely the coupled Burgers equations, which can be used to describe two-layer fluids is studied in detail. The Lie point symmetries of the model are obtained. By using the symmetries, four types of symmetry reductions are found. Some special types of exact solutions such as the rational solutions, travelling soliton solutions and non-travelling soliton solutions are explicitly given by solving the reduction equations.