Traveling Wave Solutions to the K(m,n) equation with generalized evolution Using the First Integral Method

Abstract

In this paper, we investigate the first integral method for solving the K (m, n) equation with generalized evolution.(un)+ a(um)ux + b(un)xxx = 0 t A class of traveling wave solutions for the considered equations are obtained where 4n = 3(m + 1). This idea can obtain some exactsolutions of this equations based on the theory of Commutative algebra

Keywords

• Traveling wave solutions,First integral method K (m,n) equation

References

1. P. Rosenau, J. M. Hyman, Phys.Rev. Lett. 70 (5) (1993).
2. J. H. He, Int. J Nonlinear Sci. Numer. Simulat. 6 (2) (2005).
3. J. H. He, X. H. Wu, Chaos, Solitons and Fractals 30 (3) (2006).
4. J. H. He, X. H.Wu, Chaos, Solitons and Fractals 29 (1) (2006).
5. J. H. He Int. J Modern Phys. B 20 (10) (2006).
6. L. Xu,Chaos, Solitons and Fractals 37 (1) (2008).
7. A. M. Wazwaz, Math. Comput. Simulat. 59 (6) (2002).
8. A. M. Wazwaz, Appl. Math. Comput. 132 (1) (2002).

9. Y. Chen, B. Li, H. Q. Zhang, Math. Comput. Simul. 64 (5) (2004).
10. B. He, Q. Meng, W. Rui , Y. Long, Commun. Nonlinear Sci. Numer.Simulat. 13 (2008).
11. Z. Y. Yan, Comput. Phys. Commun. 152 (1) (2003).
12. Z. Y. Yan, Comput. Phys. Commun. 153 (1) (2003).
13. A. Biswas, Phys. Lett. A 372 (25) (2008).
14. Y. G. Zhu, K. Tong, T. C. Lu, Chaos, Solitons and Fractals 33 (4) (2007).
15. C. H. Xu, L. X. Tian, Chaos, Solitons and Fractals 40 (2) (2009).
16. T. C. Xia, Appl. Math. E-Notes 3(2003).
17. D. Lu, B. Hong, L. Tian, International Journal of Nonlinear Science 2(2OO6). M.R. Miura, B¨aacklund Transformation, Springer, Berlin, 1978.
18. R. Hirota, The direct method in soliton theory, Cambridge UniversityPress, Cambridge, 2004.
19. W. Mal.iet, Am. J. Phys. 60, 7(1992).
20. A. M. Wazwaz, Appl. Math. Comput. 138 (2/3) (2003).
21. E. Fan, Phys. Lett. A. 277 (2000).
22. Ahmet Bekir, International Journal of Nonlinear Sciences and Numerical Simulation, 10, (6) 735-739. X. D. Zheng, T. C. Xia and H. Q. Zhang, Appl. Math. E-Notes 2 (2002).
23. A.M.Wazwaz, Math. and Comput. Modelling. 15 (1982).
24. F. Tascan, Ahmet Bekir,Applied Mathematics and Computation, 215 (8) (2009).
25. M. Inc, M. Ergut, Appl Math E-Notes 5 (2005).
26. H.-T. Chen, H.-Q. Zhang, Chaos Solitons Fractals 20 (2004).
27. Z. S. Feng, Phys. Lett. A. 293(2002).
28. F. Tascan, Ahmet Bekir, M. Koparan, Comm. Nonlinear Sci. Numer.Simulat. 14 (5) 1810-1815.
29. Ahmet Bekir, O. Unsal, Physica Scripta, 85 065003 (2012)
30. G. Ebadi and A. Biswas, Comm. Nonlinear Sci. Numer. Simulat. 16,2377 (2011).
31. R. S. Banerjee, Phs. Scr. 57(5), 598 (1998).
32. T.R. Ding, C.Z. Li, Ordinary Differential Equations, Peking University Press, Peking, 1996.
33. N. Bourbaki, Commutative Algebra, Addison Wesley, Paris, 1972.
34. J.H. He, X.H. Wu, Chaos Solitons Fractals. 30 (2006).
35. Ahmet Bekir, Comm. Nonlinear Sci. Numer. Simulat. 13, 9 (2008).
36. M.S. Bruz´on, M.L. Gandarias, Mathematical Methods in the Applied Science 2010, DOI: 10.1002/mma.1339.
37. M.S. Bruz´on, M.L. Gandarias, G.A. Gonz´alez, R. Hansen, Applied Mathematics and Computation vol. 218, issue 20, 2012.
38. M. J. Ablowitz and H. Segur, Solitons and inverse scattering transform, Philadelphia, SIAM, 1981.
39. B. P. Palka, An Introduction to Complex Function Theory, Spring-Verlag, New York, 1991.