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

doi:10.1088/1674-1056/20/12/120202

中国物理B ›› 2011, Vol. 20 ›› Issue (12): 120202-120202.doi: 10.1088/1674-1056/20/12/120202

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

孟凡伟¹, 张耀明², 冯青华³

(1)School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China; (2)School of Science, Shandong University of Technology, Zibo 255049, China; (3)School of Science, Shandong University of Technology, Zibo 255049, China;School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

收稿日期:2011-04-01 修回日期:2011-06-22 出版日期:2011-12-15 发布日期:2011-12-15
基金资助:
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), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20103705110003).

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

Feng Qing-Hua(冯青华)^a)b)^†, Meng Fan-Wei(孟凡伟)^b), and Zhang Yao-Ming(张耀明)^a)

^a School of Science, Shandong University of Technology, Zibo 255049, China; ^bSchool of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Received:2011-04-01 Revised:2011-06-22 Online:2011-12-15 Published:2011-12-15
Supported by:
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), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20103705110003).

摘要/Abstract

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.

关键词: first integral method, Riccati equation, nonlinear equation, traveling wave solution

Abstract: 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.

Key words: first integral method, Riccati equation, nonlinear equation, traveling wave solution

中图分类号: (Partial differential equations)

02.30.Jr

04.20.Jb (Exact solutions)

冯青华, 孟凡伟, 张耀明. Traveling wave solutions for two nonlinear evolution equations with nonlinear terms of any order[J]. 中国物理B, 2011, 20(12): 120202-120202.

Feng Qing-Hua(冯青华), Meng Fan-Wei(孟凡伟), and Zhang Yao-Ming(张耀明) . Traveling wave solutions for two nonlinear evolution equations with nonlinear terms of any order[J]. Chin. Phys. B, 2011, 20(12): 120202-120202.

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

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

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