Gardner-KP方程的孤立波解  

Various Solitary Wave Solutions to Gardner-KP Equation

作　　者：李灵晓[1] 李保安[1] 

机构地区：[1]河南科技大学数学与统计学院,河南洛阳471023

出　　处：《河南科技大学学报（自然科学版）》2016年第1期92-95,10,共4页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(11271110);河南省教育厅自然科学研究计划基金项目(2011B110013)

摘　　要：行波约化后的Gardner-KP方程,通过未知函数的倒置变换,转化为一个易于求解的非线性常微分方程(ordinary diffrential equation,ODE)。其解可选取与之紧密相关的二阶线性ODE的解而得到,进而获得Gardner-KP方程的有界钟状孤立波解、扭状孤立波解、有理函数解和无界奇异孤立波解。By reciprocal transformation of an unknown function,the Gardner-KP equation reduced by travelling wave was converted into a nonlinear ordinary differential equation( ODE) linked up with a second order linear ODE. From the general solutions of the linear ODE,the solutions of the nonlinear ODE could be derived.Therefore the bounded bell shaped solitary wave solutions,kink shaped solitary wave solutions,rational function solutions as well as various unbounded solitary wave solutions with singularities of the Gardner-KP equation were obtained.

关 键 词：Gardner-KP方程 未知函数倒置变换 钟状孤立波解 扭状孤立波解 有理函数解 奇异孤立波解 

分 类 号：O175.2[理学—数学]