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提出了利用耦合的Riccati方程组的某些特解构造非线性微分方程组精确解析解的一种方法.应用这种方法研究了两个耦合的常微分方程组,系统地获得了它们的一些精确解.给出了非线性浅水波近似方程组和非线性Schr?dinger-KdV方程组若干新的孤波解.
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关键词:
- 非线性耦合方程组 /
- Riccati方程组 /
- 符号计算 /
- 孤波
A method for constructing explicit exact solutions of coupled ordinary nonlinear differential equations by using the special solutions of Riccati equations is proposed.Two coupled nonlinear differentiall equations are studied using this method,and several new solutions (either functional or parametrical) are explicitly obtained,in addition to rederiving all known solutions in a systematic way.-
Keywords:
- coupled nonlinear differential equations /
- Riccati equations /
- symbolic computation /
- solitary wave
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