组合KdV方程的显式精确解  

Explicit and exact solutions of the combined KdV equation

作　　者：石玉仁[1] 吕克璞[1] 段文山[1] 洪学仁[1] 赵金保[1] 杨红娟[1] 

机构地区：[1]西北师范大学物理与电子工程学院,兰州730070

出　　处：《物理学报》2003年第2期267-270,共4页Acta Physica Sinica

基　　金：国家自然科学基金 (批准号 :10 2 470 0 8);西北师范大学科技创新工程 (批准号 :NWNU KJCXGC 2 15 )资助的课题~~

摘　　要：借助计算机代数系统Mathematica ,利用双曲函数法找到了组合KdV方程 (CombinedKdVEquation)的精确孤立波解 ,包括钟型孤立波解和扭结型孤立波解 .在此基础上又对双曲函数法的思想进行了推广 ,从而获得了其更多的显式精确解 ,包括间断型激波解和指数函数型解 .这种方法也适用于求解其他非线性发展方程 (组 ) .With the aid of computer algebraic system 'Mathematica' and by using the hyperbola function method, the exact and solitary wave solutions of the combined KdV equation are obtained, including the bell-like and the kink solitary wave solutions. The thought based on the hyperbola function method is extended, and more explicit and exact solutions are successfully derived, including shock wave type solutions with break point and exponential function type solutions This method can be used also to solve other nonlinear evolution equation(s).

关 键 词：组合KDV方程 双曲函数法 孤立函数法 孤立波解 精确解 非线性偏微分方程 

分 类 号：O175[理学—数学]