广义Boussinesq方程的不变集与精确解

Invariant set and exact solutions to the generalized Boussinesq equation

不变集方法是一种构造非线性偏微分方程精确解的有效方法.文章利用不变集思想方法,讨论了一类非线性偏微分方程utt=A(u)uxxxx+B(u)uxx+C(u)(uux)x+D(u)u2d的问题,得到了一些情况下对应方程的精确解,从而丰富了这类方程解的研究.

Invariant set was very effective to construct the exact solutions of the nonlinear PDEs.Using the invariant set of thinking,the generalized Boussinesq equation ut =A（u）uxxxx＋B（u）uxx＋C（u）（uux）x＋D（u）u2 was discussed,and the exact solutions to some special equations were obtained in some case.Thus the study on solution to these equations was enriched.