Boussinesq方程精确解析解研究

Study of exact analytical solutions of Boussinesq equation

应用推广的齐次平衡法获得了自Ba..cklund变换,得到了Boussinesq方程孤子解和其他新精确解.从齐次平衡法出发,可获得一个非线性变换,简化Boussinesq方程为一个线性和两个非线性偏微分方程并发现了一些特殊的精确解.在方程求解过程中采用吴方法和计算机软件Mathematica作为基本工具.

Using homogenous balance method, the autoBa··cklund transformation of Boussinesq equation and its derived equation are obtained. By analyzing the derived equation, solitary wave solutions and other abundant exact solutions are obtained. Wu algebraic elimination method and the computer software Mathematica are also basic tools during the course of solving equations.