F展开法的发展和两个广义KdV方程的孤立波解  

Progress of F-expansion Method and Solitary Wave Solutions for Two Generalized KdV Equations

作　　者：李向正[1] 李修勇[1] 

机构地区：[1]河南科技大学理学院,河南洛阳471003

出　　处：《河南科技大学学报（自然科学版）》2006年第5期90-92,共3页Journal of Henan University of Science And Technology:Natural Science

基　　金：河南省教育厅自然科学基金项目(2006110002);河南科技大学科研基金项目(2004ZD0022006ZY001)

摘　　要：对求解非线性方程的F展开法进行了综述,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,给出了一个辅助常微分方程,借助它可求解具有高次非线性项的非线性偏微分方程。作为实例,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 new progress of the method,a subsidiary ordinary differential equation that can be used to solve nonlinear partial differential equation with higher order nonlinear terms is given,by which,as illustrative examples,the solitary wave solutions for two generalized KdV equations with higher order nonlinear terms are obtained.Compared with the literature appeared,the F-expansion is simpler and the results obtained are more general.The method can also be used to solve similar nonlinear equations.

关 键 词：F展开法 齐次平衡原则 广义KDV方程 孤立波解 

分 类 号：O175.2[理学—数学]