Full Text:   <1506>

CLC number: O175.29; O241.7

On-line Access: 

Received: 2006-08-16

Revision Accepted: 2006-12-17

Crosschecked: 0000-00-00

Cited: 0

Clicked: 3360

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
1. Reference List
Open peer comments

Journal of Zhejiang University SCIENCE A 2007 Vol.8 No.4 P.660~664

10.1631/jzus.2007.A0660


Construction of solitonary and periodic solutions to some nonlinear equations using EXP-function method


Author(s):  ZHANG Mei, ZHANG Wen-jing

Affiliation(s):  Department of Applied Physics, College of Science, Donghua University, Shanghai 201620, China

Corresponding email(s):   zhmm@mail.dhu.edu.cn

Key Words:  Soliton, Periodic solution, Nonlinear equation, EXP-function method


ZHANG Mei, ZHANG Wen-jing. Construction of solitonary and periodic solutions to some nonlinear equations using EXP-function method[J]. Journal of Zhejiang University Science A, 2007, 8(4): 660~664.

@article{title="Construction of solitonary and periodic solutions to some nonlinear equations using EXP-function method",
author="ZHANG Mei, ZHANG Wen-jing",
journal="Journal of Zhejiang University Science A",
volume="8",
number="4",
pages="660~664",
year="2007",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2007.A0660"
}

%0 Journal Article
%T Construction of solitonary and periodic solutions to some nonlinear equations using EXP-function method
%A ZHANG Mei
%A ZHANG Wen-jing
%J Journal of Zhejiang University SCIENCE A
%V 8
%N 4
%P 660~664
%@ 1673-565X
%D 2007
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2007.A0660

TY - JOUR
T1 - Construction of solitonary and periodic solutions to some nonlinear equations using EXP-function method
A1 - ZHANG Mei
A1 - ZHANG Wen-jing
J0 - Journal of Zhejiang University Science A
VL - 8
IS - 4
SP - 660
EP - 664
%@ 1673-565X
Y1 - 2007
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2007.A0660


Abstract: 
This paper applies the EXP-function method to find exact solutions of various nonlinear equations. Tzitzeica-Dodd-Bullough (TDB) equation was selected to illustrate the effectiveness and convenience of the suggested method. More generalized solitonary solutions with free parameters were obtained by suitable choice of the free parameters, and also the obtained solitonary solutions can be converted into periodic solutions.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1] Abdusalam, H.A., 2005. On an improved complex tanh-function method. Int. J. Nonlinear Sci. Num. Simulation, 6(2):99-106.

[2] Bai, C.L., Zhao, H., 2006. Generalized extended tanh-function method and its application. Chaos, Solitons & Fractals, 27:1026-1035.

[3] Bildik, N., Konuralp, A., 2006. The use of Variational Iteration Method, Differential Transform Method and Adomian Decomposition Method for solving different types of nonlinear partial differential equations. Int. J. Nonlinear Sci. Num. Simulation, 7:65-70.

[4] Brezhnev, Y.V., 1996. Darboux transformation and some multi-phase solutions of the Tzitzeica-Dodd-Bullough equation. Phys. Lett. A, 211:94-100.

[5] El-Shahed, M.F., 2005. Application of He’s homotopy perturbation method to Volterra’s integro-differential equation. Int. J. Nonlinear Sci. Num. Simulation, 6(2):163-168.

[6] El-Sabbagh, M.F., Ali, A.T., 2005. New exact solutions for (3+1)-dimensional Kadomtsev-Petviashvili equation and generalized (2+1)-dimensional Boussinesq equation. Int. J. Nonlinear Sci. Num. Simulation, 6:151-162.

[7] Fan, E., Hon, Y.C., 2003. Applications of extended tanh method to ‘special’ types of nonlinear equations. Appl. Math. Comput., 141:351-358.

[8] He, J.H., 2005a. Homotopy perturbation method for bifurcation of nonlinear problems. Int. J. Nonlinear Sci. Num. Simulation, 6(2):207-208.

[9] He, J.H., 2005b. Application of homotopy perturbation method to nonlinear wave equations. Chaos, Solitons & Fractals, 26:695-700.

[10] He, J.H., 2006a. New interpretation of homotopy perturbation method. Int. J. Modern Phys. B, 20(18):2561-2568.

[11] He, J.H., 2006b. Homotopy perturbation method for solving boundary value problems. Phys. Lett. A, 350:87-88.

[12] He, J.H., 2006c. Some asymptotic methods for strongly nonlinear equations. Int. J. Modern Phys. B, 20:1141-1199.

[13] He, J.H., Abdou, M.A., 2006. New periodic solutions for nonlinear evolution equations using Exp-function method. Chaos, Solitons & Fractals, in press.

[14] He, J.H., Wu, X.H., 2006a. Construction of solitary solution and compacton-like solution by variational iteration method. Chaos, Solitons & Fractals, 29:108-113.

[15] He, J.H., Wu, X.H., 2006b. Exp-function method for nonlinear wave equations. Chaos, Solitons & Fractals, 30:700-708.

[16] Liu, H.M., 2004. Variational approach to nonlinear electrochemical system. Int. J. Nonlinear Sci. Num. Simulation, 5(1):95-96.

[17] Liu, H.M., 2005. Generalized variational principles for ion acoustic plasma waves by He’s semi-inverse method. Chaos, Solitons & Fractals, 23:573-576.

[18] Momani, S., Abuasad, S., 2006. Application of He’s variational iteration method to Helmholtz equation. Chaos, Solitons & Fractals, 27:1119-1123.

[19] Odibat, Z.M., Momani, S., 2006. Application of variational iteration method to nonlinear differential equations of fractional order. Int. J. Nonlinear Sci. Num. Simulation, 7:27-34.

[20] Pikovsky, A., Rosenau, P., 2006. Phase compactons. Phys. D: Nonlinear Phenomena, 218(1):56-69.

[21] Ren, Y.J., Zhang, H.Q., 2006. A generalized F-expansion method to find abundant families of Jacobi Elliptic Function solutions of the (2+1)-dimensional Nizhnik-Novikov-Veselov equation. Chaos, Solitons & Fractals, 27:959-979.

[22] Rosenau, P., Hyman, J.M., 1993. Compactons: solitons with finite wavelengths. Phys. Rev. Lett., 75(5):564-567.

[23] Rosenau, P., 2000. Compact and noncompact dispersive patterns. Phys. Lett. A, 275(3):193-203.

[24] Rosenau, P., 2006. On a model equation of traveling and stationary compactons. Phys. Lett. A, 356:44-50.

[25] Siddiqui, A.M., Mahmood, R., Ghori, Q.K., 2006. Thin film flow of a third grade fluid on a moving belt by He’s homotopy perturbation method. Int. J. Nonlinear Sci. Num. Simulation, 7:7-14.

[26] Wang, D.S., Zhang, H.Q., 2005. Further improved F-expansion method and new exact solutions of Konopelchenko-Dubrovsky equation. Chaos, Solitons & Fractals, 25:601-610.

[27] Wang, M.L., Li, X.Z., 2005. Extended F-expansion method and periodic wave solutions for the generalized Zakharov equations. Phys. Lett. A, 343:48-54.

[28] Wang, Q., Chen, Y., Zhang, H., 2005. A new Riccati equation rational expansion method and its application to (2+1)-dimensional Burgers equation. Chaos, Solitons & Fractals, 25(5):1019-1028.

[29] Wazwaz, A.M., 2005. The tanh method: solitons and periodic solutions for the Dodd-Bullough-Mikhailov and the Tzitzeica-Dodd-Bullough equations. Chaos, Solitons & Fractals, 25(1):55-63.

[30] Yomba, E., 2005a. The extended Fan’s sub-equation method and its application to KdV-MKdV, BKK and variant Boussinesq equations. Phys. Lett. A, 336(6):463-476.

[31] Yomba, E., 2005b. The extended F-expansion method and its application for solving the nonlinear wave, CKGZ,GDS, DS and GZ equations. Phys. Lett. A, 340(1-4):149-160.

[32] Yomba, E., 2005c. The modified extended Fan sub-equation method and its application to (2+1)-dimensional dispersive long wave equation. Chaos, Solitons & Fractals, 26:785-794.

[33] Zhang, J.L., Wang, M.L., Wang, Y.M., Fang, Z.D., 2006. The improved F-expansion method and its applications. Phys. Lett. A, 350:103-109.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - Journal of Zhejiang University-SCIENCE