Traveling Wave Solutions of the RLW-Burgers Equation and Potential Kdv Equation by Using the - Expansion Method

Abstract

Keywords

• -

Traveling Wave Solutions of the RLW-Burgers Equation and Potential Kdv Equation by Using the - Expansion Method

Abstract

Bu çalışmada, RLW-Burgers ve potansiyel KdV denklemlerinin hareket eden dalga çözümleri içinaçılım metodu sunulur. Bu metot yardımı ile yukarıda bahsedilen denklemlerin bazı hareket eden dalga çözümleri bulunur

Keywords

• RLW-Burgers denklemi, Potansiyel KdV denklemi, açılım metot, Hareket eden dalga çözümler

References

1. M. Wang, X. Li, J. Zhang, ‘The (G'/G) expansion method and traveling wave solutions of nonlinear evolutions in mathematical physics’, Physics Letters A, 372 (2008), pp. 417-423.
2. H. Zhang, ‘New application of the (G'/G) expansion method’, Communications in Nonlinear Science and Numerical Simulation, 14 (2009), pp. 3220-3225.
3. I. Aslan, T. Oziş, ‘Analytic study on two nonlinear evolution equations by using the (G'/G) expansion method’, Applied Mathematics and Computation, 209 (2009), pp. 425-429.
4. I. Aslan, T. Oziş, ‘On the validity and reliability of the (G'/G) expansion method by using higher-order nonlinear equations’, Applied Mathematics and Computation, 211 (2009), pp. 531-536.
5. A. Bekir, ‘Application of the (G'/G) expansion method for nonlinear evolution equations’, Physics Letters A, 372 (2008), pp. 3400-3406.
6. S. Zhang, W. Wang and J.L. Tong, ‘A generalized (G'/G) expansion method and its application to the (2+1) dimensional Broer-Kaup equations’, Applied Mathematics and Computation, 209 (2009), pp. 399-404.
7. S. Zhang, L.Dong, J- Mei. Ba, Y-Na Sun, ‘The (G'/G) expansion method for nonlinear differential difference equations’, Physics Letters A, 373 (2009), pp. 905-910.
8. L. Debtnath, Nonlinear Partial Differential Equations for Scientist and Engineers, (Birkhauser, Boston, MA, 1997).

9. A. M. Wazwaz, Partial Differential Equations: Methods and Applications, (Balkema, Rotterdam, 2002).
10. M. A. Abdou, S. Zhang, ‘New periodic wave solutions via extended mapping method’, Communications in Nonlinear Science and Numerical Simulation, 14 (2009), pp. 2-11.
11. M. A. Abdou, ‘New exact traveling wave solutions for the generalized nonlinear Schroedinger equation with a source’, Chaos Solitons Fractals, 38 (2008), pp. 949-955.
12. A. M. Wazwaz, ‘A study of nonlinear dispersive equations with solitary-wave solutions having compact support’, Mathematics and Computers in Simulation, 56 (2001), pp. 269-276.
13. Y. Lei, Z. Fajiang, W. Yinghai, ‘The homogeneous balance method, Lax pair, Hirota transformation and a general fifth-order KdV equation’, Chaos Solitons Fractals, 13 (2002), pp. 337-340.
14. A. H. Khater, O.H. El-Kalaawy, M.A. Helal, ‘Two new classes of exact solutions for the KdV equation via Bäcklund transformations’, Chaos, Solitons & Fractals, 12 (1997), pp. 1901-1909.
15. M. L. Wang, ‘Exact solutions for a compound KdV-Burgers equation’, Physics Letters A, 213 (1996), pp. 279-287.
16. M. L. Wang, Y. Zhou, Z. Li, ‘Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics’, Physics Letters A, 216 (1996), pp. 67-75.
17. M. A. Helal, M. S. Mehanna, ‘The tanh method and Adomian decomposition method for solving the foam drainage equation’, Applied Mathematics and Computation, 190 (2007), pp. 599-609.
18. A. M. Wazwaz, ‘The tanh and the sine-cosine methods for the complex modified KdV and the generalized KdV equations’, Computers & Mathematics with Applications, 49 (2005), pp. 1101-1112.
19. B. R. Duffy, E. J. Parkes, ‘Travelling solitary wave solutions to a seventh-order generalized KdV equation’, Physics Letters A, 214 (1996), pp. 271-272.
20. E. J. Parkes, B. R. Duffy, ‘Travelling solitary wave solutions to a compound KdV-Burgers equation’, Physics Letters A, 229 (1997), pp. 217-220.
21. A. Borhanifar, M. M. Kabir, ‘New periodic and soliton solutions by application of Exp-function method for nonlinear evolution equations’, Journal of Computational and Applied Mathematics, 229 (2009), pp. 158-167.
22. A. M. Wazwaz, ‘Multiple kink solutions and multiple singular kink solutions for two systems of coupled Burgers-type equations’, Communications in Nonlinear Science and Numerical Simulation, 14 (2009), pp. 2962-2970.
23. E. Demetriou, N. M. Ivanova, C. Sophocleous, ‘Group analysis of (2+1)-and (3+1) dimensional diffusion-convection equations’, Journal of Mathematical Analysis and Applications, 348 (2008), pp. 55-65.
24. D. S. Wang, H. Li, ‘Single and multi-solitary wave solutions to a class of nonlinear evolution equations’, Journal of Mathematical Analysis and Applications, 343 (2008), pp. 273-298.
25. T. Oziş, A. Yıldırım, ‘Reliable analysis for obtaining exact soliton solutions of nonlinear Schrödinger (NLS) equation’, Chaos,Solitons & Fractals, 38 (2008), pp. 209-212.
26. A.Yıldırım, ‘Application of He s homotopy perturbation method for solving the Cauchy reactiondiffusion problem’, Computers & Mathematics with Applications, 57 (2009), pp. 612-618.
27. A.Yıldırım, ‘Variational iteration method for modified Camassa-Holm and Degasperis-Procesi equations’, Communications in Numerical Methods in Engineering, (2008) (in press).
28. T.Oziş, A.Yıldırım, ‘Comparison between Adomian’s method and He’s homotopy perturbation method’, Computers & Mathematics with Applications, 56 (2008), pp. 1216-1224.
29. A.Yıldırım, ‘An Algorithm for Solving the Fractional Nonlinear Schrödinger Equation by Means of the Homotopy Perturbation Method’, International Journal of Nonlinear Sciences and Numerical Simulation, 10 (2009), pp. 445-451.
30. W. Hereman, A. Korpel and P.P. Banerjee, Wave Motion 7 (1985), pp. 283-289.
31. W. Hereman and M. Takaoka, ‘Solitary wave solutions of nonlinear evolution and wave equations using a direct method and MACSYMA’, Journal of Physics A: Mathematical and General 23 (1990), pp. 4805-4822.
32. H. Lan and K. Wang, ‘Exact solutions for two nonlinear equations’, Journal of Physics A: Mathematical and General 23 (1990), pp. 3923-3928.
33. S. Lou, G. Huang and H. Ruan, ‘Exact solitary waves in a convecting fluid’, Journal of Physics A: Mathematical and General 24 (1991), pp. L587-L590.
34. W. Malfliet, ‘Solitary wave solutions of nonlinear wave equations’, American Journal of Physics 60 (1992), pp. 650-654.
35. E. J. Parkes and B. R. Duffy, ‘An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations’, Computer Physics Communications 98 (1996), pp. 288-300.
36. E. Fan, ‘Extended tanh-function method and its applications to nonlinear equations’, Physics Letters A 277 (2000), pp. 212-218.
37. S. A. Elwakil, S. K. El-labany, M. A. Zahran and R. Sabry, ‘Modified extended tanh-function method for solving nonlinear partial differential equations’, Physics Letters A 299 (2002), pp. 179-188.
38. X. Zheng, Y. Chen and H. Zhang, ‘Generalized extended tanh-function method and its application to (1+1)-dimensional dispersive long wave equation’, Physics Letters A 311 (2003), pp. 145-157.
39. E. Yomba, ‘Construction of new soliton-like solutions of the (2+1) dimensional dispersive long wave equation’, Chaos, Solitons & Fractals, 20 (2004), pp. 1135-1139.
40. H. Chen and H. Zhang, ‘New multiple soliton solutions to the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation’, Chaos, Solitons & Fractals, 19 (2004), pp. 71-76.