一类反应扩散方程的精确解

Exact Solutions for a Kind of Reaction Diffusion Equations

中文关键词:  反应扩散方程  首次积分法  精确解.

英文关键词:reaction diffusion equations  first integral method  exact solutions.

中文摘要:

      运用首次积分法并借助计算机符号计算系统Mathematica得到了一类非线性反应扩散方程$u_t-u_{xx}+\alpha u+\beta u^2+\gamma u^3=0$的精确解,其中既包括已知的类孤立波解,又有新的精确解.

英文摘要:

      Applying a new method called the first integral method, we obtain some exact solutions of a kind of reaction diffusion equations $u_t - u_{xx} + \alpha\, u + \beta\, u^2 + \gamma\, u^3 = 0$. These solutions not only include the soliton solutions that obtained in the previous literature, but also include some new exact solutions.