New exact solutions to a class of coupled nonlinear PDEs

International Journal of Nonlinear Sciences and Numerical Simulation

Volumn 10, Issue 6, 2009, Pages 779-796

  Mokhtari, Reza ^a   Mohammadi, Maryam ^a  

^a ISFAHAN UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Auxiliary ordinary differential equation; Coupled NLPDEs; Exact travelling wave solutions; Exp function method; Generalized Riccati equation

Indexed keywords

EID: 69149092516     PISSN: 15651339     EISSN: None     Source Type: Journal    
DOI: 10.1515/IJNSNS.2009.10.6.779     Document Type: Article

References (35)

1. Yusufoǧlu E, Bekir A. Exact solutions of coupled nonlinear Klein-Gordon equations, Math. Comput. Modelling. 48 (2008) 16941700.
2. Fan E. Soliton solutions for a generalized Hirota-Satsuma coupled KdV equation and a coupled MKdV equation, Phys. Lett. A. 282 (2001) 18-22
3. Bekir A. New exact travelling wave solutions of some complex nonlinear equations, Commun.Nonlinear Sci. Numer. Simul. 14 (2009)1069-1077.
4. Al-Khaled K, Al-Refai M, Alawneh A. Traveling wave solutions using the variational method and the tanh method for nonlinear coupled equations, Appl. Math. Comput. 202 (2008) 233-242.
5. Wazwaz A.M. Multiple-front solutions for the Burgers equation and the coupled Burgers equations, Appl. Math. Comput. 190 (2007)1198-1206.
6. Bekir A. Applications of the extended tanh method for coupled nonlinear evolution equations, Commun. Nonlinear Sci. Numer. Simul. 13 (2008) 1748-1757.
7. He J.H, Wu X.H. Exp-function method for nonlinear wave equations, Chaos Soliton Fract. 30 (2006) 700-708.
8. Bekir A, Boz A. Exact Solutions for a Class of Nonlinear Partial Differential Equations using Exp-Function Method, Int. J. Nonlinear Sci. Numer. Simul. 8 (2007) 505-513.
9. Zhou X.W, Wen Y.X, He J.H. Exp-function method to solve the nonlinear dispersive K(m,n) equations, Int. J. Nonlinear Sci. Numer. Simul. 9 (2008) 301-306.
10. Zhu S.D. Exp-function Method for the Hybrid-Lattice System, Int. J. Nonlinear Sci. Numer.Simul. 8 (3) (2007) 461-465.
11. Zhu S.D. Exp-function Method for the Discrete mKdV Lattice, Int. J. Nonlinear Sci. Numer. Simul. 8 (3) (2007) 465-468.
12. He J.H, Zhang L.N. Generalized solitary solution and compacton-like solution of the Jaulent-Miodek equations using the Expfunction method, Phys. Lett. A. 372 (2008) 1044-1047.
13. El-Wakil S.A, Abdou M.A. Modified extended tanh-function method for solving nonlinear partial differential equations, Chaos Soliton Fract. 31 (2007) 1256-1264.
14. Soliman A.A. The modified extended tanhfunction method for solving Burgers-type equations, Physica A. 361 (2006) 394-404.
15. Elwakil S.A, El-labany S.K, Zahran M.A, Sabry R. Modified extended tanh-function method for solving nonlinear partial differential equations, Phys. Lett. A. 299 (2002) 179-188.
16. Ali A.H.A, Soliman A.A, Raslan K.R. Soliton solution for nonlinear partial differential equations by cosine-function method, Phys. Lett. A. 368 (2007) 299-304.
17. Yomba E. The extended Fan's sub-equation method and its application to KdV-MKdV, BKK and variant Boussinesq equations, Phys. Lett. A. 336 (2005) 463-476.
18. Ganji D.D, Rafei M. Solitary wave solutions for a generalized Hirota-Satsuma coupled KdV equation by homotopy perturbation method, Phys. Lett. A. 356 (2006) 131-137.
19. Fan E, Zhang H. New exact solutions to a system of coupled KdV equations, Phys. Lett. A. 245 (1998) 389-392.
20. Kaya D. Solitary wave solutions for a generalized Hirota-Satsuma coupled KdV equation, Appl. Math. Comput. 147 (2004) 69-78.
21. Dai C.Q, Wang Y.Y. New exact solutions of the (3+l)-dimensional Burgers system, Phys Lett A. 373 (2009) 181-187.
22. Li X, Wang M. A sub-ODE method for finding exact solutions of a generalized KdV-mKdV equation with high-order terms, Phys. Lett. A. 361 (2007) 115-118.
23. Yang Z. New exact travelling wave solutions for two potential coupled KdV equations with symbolic computation, Chaos Soliton Fract. 34 (2007) 932-939.
24. Zhu S.D. The generalizing Riccati equation mapping method in nonlinear evolution equation:application to (2 + l)-dimensional BoitiLeon-Pempinelle equation, Chaos Soliton Fract. 37 (2008) 1335-1342.
25. Zhang H. New exact travelling wave solutions to the complex coupled KdV equations and modified KdV equation, Commun. Nonlinear Sci. Numer. Simul. 13 (2008) 1776-1781.
26. Zhang H. New exact solutions for two generalized Hirota-Satsuma coupled KdV systems, Commun. Nonlinear Sci. Numer. Simul. 12 (2007) 1120-1127.
27. Darwish A, Fan E.G. A series of new explicit exact solutions for the coupled KleinGordon-Schrödinger equations, Chaos Soliton Fract. 20 (2004) 609-617.
28. Xie F.D, Yuan Z.T. Computer algebra and solutions to the Karamoto-Sivashinsky equation, Commun. Theor. Phys. 43 (2005)
29. Sirendaoreji. Auxiliary equation method and new solutions of Klein-Gordon equations, Chaos Soliton Fract. 31 (2007) 943-950.
30. Esipov S.E. Coupled Burgers' equations: a model of polydispersive sedimentation, Phys. Rev. E 52 (1995) 3711-3718.
31. Ma Z.Y, Wu X.F, Zhu J.M. Multisoliton excitations for the Kadomtsev-Petviashvili equation and the coupled Burgers equation, Chaos Soliton Fract. 31 (2007) 648-657.
32. Ma W.X. A hierarchy of coupled Burgers systems possessing a hereditary structure, J. Phys. A: Math. Gen. 26 (1993) 1169-1174.
33. Chen R, WU Z. Solving partial differential equation by using multiquadric quasiinterpolation, Appl. Math. Comput. 186 (2007) 1502-1510.
34. Boiti M, Leon J.Jp, Pempinelli F. Integrable two-dimensional generalization of the sineand sinh-Gordon equations, Inverse Problems. 3 (1987) 37-49.
35. Wu Y, Geng X, Hu X, Zhu S. A generalized Hirota Satsuma coupled Korteweg-de Vries equation and Miura transformations, Phys. Lett. A. 255 (1999) 259-264.