Traveling wave solutions for two nonlinear evolution equations with nonlinear terms of any order  

作　　者：冯青华 孟凡伟 张耀明 

机构地区：[1]School of Science,Shandong University of Technology [2]School of Mathematical Sciences,Qufu Normal University

出　　处：《Chinese Physics B》2011年第12期17-25,共9页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Grant No. 10571110);the Natural Science Foundation of Shandong Province of China (Grant Nos. ZR2009AM011 and ZR2010AZ003);the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20103705110003)

摘　　要：In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation （ODE） method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin-Bona-Mahoney equation. As a result, some traveling wave solutions for the two nonlinear equations are established successfully. Also we make a comparison between the two methods. It turns out that the Riccati sub-ODE method is more effective than the first integral method in handling the proposed problems, and more general solutions are constructed by the Riccati sub-ODE method.In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation （ODE） method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin-Bona-Mahoney equation. As a result, some traveling wave solutions for the two nonlinear equations are established successfully. Also we make a comparison between the two methods. It turns out that the Riccati sub-ODE method is more effective than the first integral method in handling the proposed problems, and more general solutions are constructed by the Riccati sub-ODE method.

关 键 词：first integral method Riccati equation nonlinear equation traveling wave solution 

分 类 号：O411.1[理学—理论物理] O175[理学—物理]