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

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

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.

Keywords: first integral method Riccati equation nonlinear equation traveling wave solution

Received: 01 April 2011
Revised: 22 June 2011
Accepted manuscript online:

PACS:	02.30.Jr	(Partial differential equations)
	04.20.Jb	(Exact solutions)

Fund: 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).

Cite this article:

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 2011 Chin. Phys. B 20 120202

[1]	Wang M L 1995 Phys. Lett. A 199 169
[2]	Shang Y D, Huang Y and Yuan W J 2008 Comput. Math. Appl. bf56 1441
[3]	Wazwaz A M 2007 Commun. Nonlinear Sci. Numer. Simul. 12 314
[4]	Wazwaz A M 2005 Comput. Math. Appl. 50 1685
[5]	Abdou M A 2007 Appl. Math. Comput. 190 988
[6]	Fan E G 2000 Phys. Lett. A 277 212
[7]	Ablowitz M J and Clarkson P A 1991 Solitons, Nonlinear Evolution Equations and Inverse Scattering (New York: Cambridge University Press)
[8]	Miura M R 1978 Bäcklund Transformation (Berlin: Springer-Verlag)
[9]	Shin B C, Darvishi M T and Barati A 2009 Comput. Math. Appl. 58 2147
[10]	Zha Q L and Li Z B 2008 Chin. Phys. B 17 2333
[11]	Zuo J M and Zhang Y M 2011 Chin. Phys. B 20 010205
[12]	Wu J P 2010 Commun. Theor. Phys. bf53 812
[13]	Emmanuel Y 2006 Chaos, Solitons and Fractals 27 187
[14]	Lu D C and Liu C L 2010 Appl. Math. Comput. 217 1404
[15]	Li X Z and Wang M L 2007 Phys. Lett. A 361 115
[16]	Wazwaz A M 2007 Commun. Nonlinear Sci. Numer. Simul. 12 1395
[17]	Wazwaz A M 2006 Phys. Lett. A 355 358
[18]	Wazwaz A M and Helal M A 2005 Chaos, Solitons and Fractals 26 767
[19]	Nickel J 2006 Phys. Lett. A 364 221
[20]	Tang Y, Xu W, Gao L and Shen J 2007 Chaos, Solitons and Fractals bf32 1846
[21]	Chen Y, Li B and Zhang H Q 2005 Commun. Nonlinear Sci. Numer. Simul. 10 133
[22]	Estevez P G, Kuru S and Negro J 2009 Chaos, Solitons and Fractals 40 2031
[23]	Feng Z S 2002 J. Phys. A: Math. Gen. 35 343
[24]	Feng Z S and Wang X H 2003 Phys. Lett. A 308 173
[25]	Lu B, Zhang H Q and Xie F D 2010 Appl. Math. Comput. 216 1329
[26]	Yang X L and Tang J S 2008 Acta Phys. Sin. 57 3305 (in Chinese)
[27]	Taogetusang and Sirendaoerji 2009 Acta Phys. Sin. 58 5894 (in Chinese)
[28]	Taogetusang, Sirendaoerji and Li S M 2010 Chin. Phys. B 19 080303
[29]	Wang J 2010 Acta Phys. Sin. 59 2924 (in Chinese)

[1]	Nonlinear dynamical wave structures of Zoomeron equation for population models Ahmet Bekir and Emad H M Zahran. Chin. Phys. B, 2022, 31(6): 060401.
[2]	Novel traveling wave solutions and stability analysis of perturbed Kaup-Newell Schrödinger dynamical model and its applications Xiaoyong Qian(钱骁勇), Dianchen Lu(卢殿臣), Muhammad Arshad, and Khurrem Shehzad. Chin. Phys. B, 2021, 30(2): 020201.
[3]	Bifurcation analysis and exact traveling wave solutions for (2+1)-dimensional generalized modified dispersive water wave equation Ming Song(宋明)†, Beidan Wang(王贝丹), and Jun Cao(曹军). Chin. Phys. B, 2020, 29(10): 100206.
[4]	Dynamics of traveling wave solutions to a highly nonlinear Fujimoto-Watanabe equation Li-Juan Shi(师利娟), Zhen-Shu Wen(温振庶). Chin. Phys. B, 2019, 28(4): 040201.
[5]	Dynamical behaviors of traveling wave solutions to a Fujimoto-Watanabe equation Zhen-Shu Wen(温振庶), Li-Juan Shi(师利娟). Chin. Phys. B, 2018, 27(9): 090201.
[6]	Fusion, fission, and annihilation of complex waves for the (2+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff system Zhu Wei-Ting (朱维婷), Ma Song-Hua (马松华), Fang Jian-Ping (方建平), Ma Zheng-Yi (马正义), Zhu Hai-Ping (朱海平). Chin. Phys. B, 2014, 23(6): 060505.
[7]	On the exact solutions to the long–short-wave interaction system Fan Hui-Ling (范慧玲), Fan Xue-Fei (范雪飞), Li Xin (李欣). Chin. Phys. B, 2014, 23(2): 020201.
[8]	Novel loop-like solitons for generalized Vakhnenko equation Zhang Min (张旻), Ma Yu-Lan (马玉兰), Li Bang-Qing (李帮庆). Chin. Phys. B, 2013, 22(3): 030511.
[9]	Applications of the first integral method to nonlinear evolution equations Filiz Tacscan and Ahmet Bekir . Chin. Phys. B, 2010, 19(8): 080201.
[10]	New application to Riccati equation Taogetusang(套格图桑), Sirendaoerji(斯仁道尔吉), and Li Shu-Min(李姝敏). Chin. Phys. B, 2010, 19(8): 080303.
[11]	Some discussions about the variable separating method for solving nonlinear models Ruan Hang-Yu(阮航宇). Chin. Phys. B, 2010, 19(5): 050204.
[12]	A connection between the (G'/G)-expansion method and the truncated Painlevé expansion method and its application to the mKdV equation Zhao Yin-Long (赵银龙), Liu Yin-Ping (柳银萍), and Li Zhi-Bin (李志斌). Chin. Phys. B, 2010, 19(3): 030306.
[13]	Travelling solitary wave solutions for the generalized Burgers--Huxley equation with nonlinear terms of any order Deng Xi-Jun(邓习军), Yan Zi-Zong(燕子宗), and Han Li-Bo(韩立波). Chin. Phys. B, 2009, 18(8): 3169-3173.
[14]	Some new exact solutions to the Burgers--Fisher equation and generalized Burgers--Fisher equation Jiang Lu(姜璐), Guo Yu-Cui(郭玉翠), and Xu Shu-Jiang(徐淑奖). Chin. Phys. B, 2007, 16(9): 2514-2522.
[15]	The projective Riccati equation expansion method and variable separation solutions for the nonlinear physical differential equation in physics Ma Zheng-Yi(马正义). Chin. Phys. B, 2007, 16(7): 1848-1854.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

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

Cite this article:

Online attention