New exact and explicit travelling wave solutions for the coupled higgs equation and a nonlinear variant of the PHI-four equation

International Journal of Nonlinear Sciences and Numerical Simulation

Volumn 11, Issue 9, 2010, Pages 725-741

  Khajeh, A ^a   Kabir, M M ^a   Yousefi Koma, A ^b  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

^b UNIVERSITY OF TEHRAN   (Iran)

Author keywords

Coupled higgs equation; Exp function method; Periodic solutions; Solitons; Travelling wave solutions; Variant of the phi four equation

Indexed keywords

EID: 78650064708     PISSN: 15651339     EISSN: None     Source Type: Journal    
DOI: 10.1515/IJNSNS.2010.11.9.725     Document Type: Article

References (40)

1. He JH. Variational iteration method - a kind of non-linear analytical technique: a) some examples. Int. J.Non-linear Mech, 1999; 34(4):699.
2. He JH. Approximate analytical solution for seepage flow with fractional derivatives in porous media. Comput Methods Appl Mech Eng. 1998; 167: 57-68.
3. He JH. Variational iteration method - Some recent results and new interpretations. J. Computational and Applied Mathematics 207 (2007): 3-17.
4. Odibat ZM, Momani S. Int. J. Nonlinear. Sci Numer Simul, 2006; 7(1): 27.
5. He JH. A coupling method of a homotopy technique and a perturbation technique for non-linear problems. Int. J. Non-Linear Mechanics 35 (2000): 37-43.
6. He JH. New interpretation of homotopy perturbation method. Int J Mod Phys B 2006; 20(18):2561-8.
7. He JH. Application of homotopy perturbation method to nonlinear wave equations. Chaos, Solitons & Fractals 2005; 26(3):695-700.
8. Siddiqui AM, Mahmood R, Ghori QK. Thin film flow of a third grade fluid on a moving belt by He's homotopy perturbation method. Int J Nonlinear Sci Numer Simul 2006; 7(1):7-14.
9. Donald Ariel P., Homotopy Perturbation Method and the Natural Convection Flow of a Third Grade Fluid through a Circular Tube, Nonlinear Science Letters A 2010; 1(1): 43-52.
10. Wang SQ, He JH. Nonlinear oscillator with discontinuity by parameter-expansion method. Chaos, Solitons & Fractals 2008; 35(4):688-691.
11. He JH, Shou DH. Application of parameter-expanding method to strongly nonlinear oscillators. Int J Nonlinear Sei Numer Simul 8 (2007): 121-124.
12. Ablowitz MJ, Segur H. Solitons and inverse scattering transform. Philadelphia: SIAM; 1981.
13. Bai CL, Zhao H. Generalized extended tanh-function method and its application. Chaos, Solitons & Fractals 2006; 27:1026-35.
14. Zayed E.M.E., Abdel Rahman H.M., The Extended Tanh-method for Finding Traveling Wave Solutions of Nonlinear Partial Differential Equations, Nonlinear Science Letters A 2010; 1(2): 193-200.
15. Adomian G. Solving Frontier Problems on Physics: The Decomposition Method, Kluwer Academic, Dordrecht, 1994.
16. Wazwaz AM. A sine-cosine method for handling nonlinear wave equations. Math Comput Model 2004; 40:499-508.
17. Yusufoglu E, Bekir A. Solitons and periodic solutions of coupled nonlinear evolution equations by using sine-cosine method. Int J Comput Math 2006; 83(12): 915-24.
18. Abdou MA. Further improved F-expansion and new exact solutions for nonlinear evolution equations. Nonlinear Dynam 2008; 52(3):277-88.
19. Zhang S. Chaos Solitons Fractals 33 (2007)1375.
20. Yomba E. The extended Fan's subequation method and its application to KdV-MKdV, BKK and variant Boussinesq equations. Phys Lett A 2005; 336:463-76.
21. He JH, Wu XH. Exp-function method for nonlinear wave equations. Chaos, Solitons & Fractals 2006; 30(3):700-8.
22. He JH. Non-Perturbative Methods for Strongly Nonlinear Problems, Dissertation. de-Verlag im Internet GmbH, Berlin, 2006.
23. Zhu SD. Exp-function method for the hybrid-lattice system. Int J Non Sci Numer Simul 2007; 8(3):461-4.
24. He JH, Abdou M.A., New periodic solutions for nonlinear evolution equations using Exp-function method, Chaos Solitons Fractals 34 (2007) 1421.
25. Wu X.H, He JH, Comput. Math. Appl. 54 (2007) 966.
26. Borhanifar A, Kabir M.M., New periodic and soliton solutions by application of Exp-function method for nonlinear evolution equations, J. Computational & Applied Mathematics 229 (2009) 158-167.
27. Borhanifar A, Kabir M.M., Vahdat Maryam. New periodic and soliton wave solutions for the generalized Zakharov system and (2 + 1)-dimensional NizhnikNovikov-Veselov system. Chaos, Solitons & Fractals 42 (2009) 1646-1654.
28. Kabir M.M., Khajeh A., New explicit solutions for the Vakhnenko and a generalized form of the nonlinear heat conduction equations via Exp-function method. Int J Nonlinear Sciences & Numerical Simulation 2009, 10(10), 1307-1318.
29. Zhang S., Nonlinear Dyn. 52 (2008) 11.
30. He JH, Zhang LN., Generalized solitary solution and compacton-like solution of the Jaulent-Miodek equations using the Exp-function method, Phys. Lett. A 372 (2008) 1044-1047.
31. Zhang S., Exp-function Method: Solitary, Periodic and Rational Wave Solutions of Nonlinear Evolution Equations, Nonlinear Science Letters A 2010; 1(2): 143-146.
32. Tajiri M. On N-soliton solutions of coupled Higgs field equations. J Phys Soc Jpn (1983); 52: 2277.
33. Hon YC, Fan EG. A series of exact solutions for coupled Higgs field equation and coupled Schrödinger-Boussinesq equation. Nonlinear Analysis 71 (2009) 3501-3508.
34. Bekir A. New exact travelling wave solutions of some complex nonlinear equations. Commun Nonlinear Sei Numer Simulat 14(2009) 1069-1077.
35. Zhao H. Applications of the generalized algebraic method to special-type nonlinear equations. Chaos, Solitons Fract 2008; 36:359-69.
36. Dashen R.F., Hasslacher B., Neveu A., Particle spectrum in model field theories from semi-classical functional integral technique, Physical Review D 11 (1975) 3424-3450.
37. Wazwaz AM., Analytic study on nonlinear variants of the RLW and the PHI-four equations. Communications in Nonlinear Science and Numerical Simulation 12 (2007) 314-327.
38. Soliman A.A., Exact traveling wave solution of nonlinear variants of the RLW and the PHI-four equations. Physics Letters A 368 (2007) 383-390.
39. Deng X, Zhao M, Li X. Travelling wave solutions for a nonlinear variant of the PHI-four equation. Mathematical and Computer Modelling 49 (2009) 617-622.
40. Wu XH, He JH. Solitary solutions, periodic solutions and compacton-like solutions using the Exp-function method. Computers and Mathematics with Applications 54 (2007) 966-986.