一类非线性演化方程的精确解析解

Exact analytic solutions for one class of nonlinear evolution equations

用直接方法结合假设方法求出一类非常广泛的非线性演化方程ut+αuux +βuxx+γuxxt+μ(uux) x +δuxxxx =0的一些显式精确解析解 ,这些解包括对流 Cahn- Hilliard方程的扭状孤立波解、奇异行波解、周期的三角函数波解 ,对流粘性 Cahn- Hilliard方程的钟状孤立波解、扭状孤立波解、2种形式的奇异行波解、周期的三角函数波解 ,带耗散项的 BBM- Burgers方程的扭状孤立波解、奇异行波解及周期的三角函数波解。

Some explicit and exact analytic solutions of the one class of nonlinear evolution equations u t+αuu x+βu xx +γu xxt +μ(uu x) x+δu xxxx =0 are obtained by a combination of the direct and the assumption method.The solutions include kink shaped solitary wave solutions,strange travelling wave solutions,and periodic trigular function wave solutions of the Cahn Hilliard equation with convective term;the bell shaped form and the kink shaped form solitary wave solutions,two types of strange travelling wave solutions,and two types periodic trigular function solutions of the convective viscous Cahn Hilliard equation:the kink shaped solitary wave solutions,strange travelling wave solutions,and the periodic trigular function wave solutions of the BBM Burgers equation with dissipative term.