6阶KdV方程的精确解  

Exact Solutions for Six-order KdV Equation

作　　者：李灵晓[1] 李二强[1] 

机构地区：[1]河南科技大学数学与统计学院,河南洛阳471003

出　　处：《河南科技大学学报（自然科学版）》2011年第4期83-86,112,共4页Journal of Henan University of Science And Technology:Natural Science

基　　金：河南省国际合作交流基金项目(084300510060);河南科技大学青年科研基金项目(2008QN026)

摘　　要：借助于6阶KdV方程的分解式,运用最近提出的(G'/G)-展开法获得了6阶KdV方程的行波解,分别以含两个任意参数的双曲函数、三角函数及有理函数表示,并运用变换方程方法得到了该6阶KdV方程的多孤子解。结合解的图形对所获得的2-孤子解做了细致的分析,讨论了两个孤波的相互作用。By means of the decomposition formula of the nonlinear six-order KdV equation and using the(G'/G)-expansion method proposed presently,travelling wave solutions of the six-order KdV equation are obtained.The solutions are expressed by hyperbolic functions,trigonometric functions and rational functions contained two arbitrary parameters.With the aid of the equation transformation method,multiple soliton solutions are also obtained.By the graphics of the solution,the two-soliton solution is analyzed in detail,and the interaction of two solitary waves is discussed.

关 键 词：6阶KdV方程 位势KdV方程 (G'/G)-展开法 变换方程方法 孤子解 齐次平衡 

分 类 号：O175.2[理学—数学]