摘要
对求解非线性方程的F展开法进行了综合论述,揭示了方法的内在本质,指出了F展开法可能的发展方向,并结合F展开法的最新进展,给出了求解具有高次非线性项的非线性偏微分方程的一个辅助常微分方程作为说明的例子,用其得到了两个具有高次非线性项的广义KdV方程的孤立波解。与已有文献相比较,这种方法更简练,结果更具有一般性.对于类似的方程同样可以用此方法求其解。
The F- expansion method which can be used to solve nonlinear equations has been summarized, the internal essence of the method has been brought to light, and the several possible improved aspects of the method have been pointed out. Based on the newly progress of the method a subsidiary ordinary differential equation that can be used to solve nonlinear partial differential equation with higher order nonlinear terms has been given, by which, as illustrative examples, the solitary wave solutions for two generalized KdV equations with higher order nonlinear terms have been obtained. Compared with the literature appeared one concludes that F - expansion is simpler and the results obtained are mere general. The method can also be used to solve similar nonlinear equations.
出处
《平顶山工学院学报》
2006年第4期42-45,共4页
Journal of Pingdingshan Institute of Technology
基金
河南省教育厅自然科学基金资助项目(2006110002)
河南科技大学科研基金资助项目(2004ZD0022006ZY001)
关键词
齐次平衡原则
F展开法
广义KDV方程
孤立波解
Homogeneous balance finciple
F-expansion method
Generalized KdV Equation
solitary wave solution
