Exp-Function Method for the Some Nonlinear Partial Dicerential Equations

[1] Debtnath, L. Nonlinear Partial Di¤erential Equations for Scientist and Engineers (Birkhauser
Boston, MA, 1997).
[2] Wazwaz, A.M. Partial Di¤erential Equations: Methods and Applications (Balkema, Rotterdam,
2002).
[3] Mal‡iet, W. Solitary wave solutions of nonlinear wave equations, Am. J. Phys. 60,
650-654, 1992.
[4] Parkes, E.J., Du¤y, B.R. An automated tanh-function method for …nding solitary wave
solutions to non-linear evolution equations, Comput. Phys. Commun. 98, 288-300, 1996.
[5] Fan, E. Extended tanh-function method and its applications to nonlinear equations, Phys.
Lett. A 277, 212-218, 2000.
[6] Fu, Z., Liu, S., Liu, S. and Zhao, Q. New Jacobi elliptic function expansion and new
periodic solutions of nonlinear wave equations, Phys. Lett. A 290, 72-76, 2001.
[7] Elwakil, S.A., El-labany, S.K., Zahran, M.A. and Sabry, R. Modi…ed extended tanhfunction
method for solving nonlinear partial di¤erential equations, Phys. Lett. A 299, 179-188,
2002.
[8] Zheng, X., Chen, Y. and Zhang, H. Generalized extended tanh-function method and its
application to (1+1)-dimensional dispersive long wave equation, Phys. Lett. A 311, 145-157,
2003.
[9] Shen S., Pan, Z. A note on the Jacobi elliptic function expansion method, Phys. Lett. A
308, 143-148, 2003.
[10] Chen, H., Zhang, H. New multiple soliton solutions to the general Burgers-Fisher equation
and the Kuramoto-Sivashinsky equation, Chaos Solitons Frac. 19, 71-76, 2004.
[11] Chen, H.T., Hong-Qing, Z. New double periodic and multiple soliton solutions of the
generalized (2 + 1)-dimensional Boussinesq equation, Chaos Solitons Frac. 20, 765-769, 2004.
68 Yavuz UGURLU
[12] Chen, Y., Wang, Q. and Li B. Jacobi elliptic function rational expansion method with
symbolic computation to construct new doubly periodic solutions of nonlinear evolution equations,
Z. Nat. Forsch. A 59, 529-536, 2004.
[13] Chen, Y., Yan, Z. The Weierstrass elliptic function expansion method and its applications
in nonlinear wave equations, Chaos Solitons Frac. 29, 948-964, 2006.
[14] He, J.H., Wu, X.H. Exp-function method for nonlinear wave equations, Chaos Solitons
Frac. 30, 700-708, 2006.
[15] Wang, M., Li, X. and Zhang, J. The G’/G-expansion method and travelling wave solutions
of nonlinear evolution equations in mathematical physics, Phys. Lett. A 372, 417-423,
2008.
[16] Guo, S., Zhou, Y. The extended G’/G-expansion method and its applications to the
Whitham–Broer–Kaup–Like equations and coupled Hirota–Satsuma KdV equations, Appl. Math.
Comput. 215, 3214-3221, 2010.
[17] Lü, H.L., Liu, X.Q. and Niu, L. A generalized G’/G-expansion method and its applications
to nonlinear evolution equations, Appl. Math. Comput. 215, 3811-3816, 2010.
[18] Ta¸scan, F. and Bekir, A. Travelling wave solutions of the Cahn–Allen equation by using
…rst integral method, Appl. Math. Comput. 207, 279-282, 2009.
[19] U¼gurlu, Y. and Kaya, D. Analytic method for solitary solutions of some partial di¤erential
equations, Phys. Lett. A 370, 251–259, 2007.
[20] Abbasbandy, S. Soliton solutions for the Fitzhugh–Nagumo equation with the homotopy
analysis method, Appl. Math. Model. 32, 2706–2714, 2008.
[21] Zhou, X. W., Wen, Y. X. and He, J.H. Exp-function method to solve the nonlinear
dispersive K(m,n) equations, Int. J. Nonlin. Sci. Num. 9 301–306, 2008.
[22] Dai, C. Q. and Wang, Y. Y. Exact travelling wave solutions of the discrete nonlinear
Schrödinger equation and the hybrid lattice equation obtained via the exp-function method, Phys.
Scripta 78, 015013, 2008.
[23] Xu, F. A. A Generalized Soliton Solution of the Konopelchenko-Dubrovsky Equation
using He’s Exp-Function Method, Z. Nat. Forsch. A 62, 685–688, 2007.
[24] Zhang, S. Explicit and Exact Nontravelling Wave Solutions of Konopelchenko-Dubrovsky
Equations, Z. Nat. Forsch. A 62 689–697, 2007.
[25] Xu, F. Application of Exp-function method to Symmetric Regularized Long Wave (SRLW)
equation, Phys. Lett. A 372 252–257, 2008.
[26] Köro¼glu, C. and Ozi¸s, T. A novel traveling wave solution for Ostrovsky equation using
Exp-function method, Comput. Math. Appl. 58, 2142-2146, 2009.
[27] Wu, X. H. and He, J. H. Solitary solutions, periodic solutions and compacton-like solutions
using the Exp-function method, Comput. Math. Appl. 54, 966-986, 2007.
[28] Kaya, D. and Inan, I. E. Exact solutions to the various nonlinear evolution equations,
Phys. Scripta 79, 045005, 2009.
[29] He, J. H. and Zhang, L. N. Generalized solitary solution and compacton-like solution of
the Jaulent–Miodek equations using the Exp-function method, Phys. Lett. A 372, 1044–1047,
2008.
[30] He, J. H. and Wu, X. H. Exp-function method for nonlinear wave equations, Chaos
Solitons Frac. 30, 700-708, 2006.
Exp-Function Method for the Some Nonlinear Partial Differential Equations 69
[31] Inan, I. E. and U¼gurlu, Y. Exp-function method for the exact solutions of …fth order
KdV equation and modi…ed Burgers equation, Appl. Math. Comput. In Press, 2009.
[32] Boz, A. and Bekir, A. Application of Exp-function method for (3+1)-dimensional nonlinear
evolution equations, Comput. Math. Appl. 56, 1451-1456, 2008.
[33] Yusufo¼glu, E. New solitonary solutions for the MBBM equations using Exp-function
method, Phys. Lett. A 372, 442-446, 2008.
[34] Wazwaz, A. M. Solitary wave solutions of the generalized shallow water wave (GSWW)
equation by Hirota’s method, tanh–coth method and Exp-function method, Appl. Math. Comput.
202, 275-286, 2008.
[35] Huaying, L. and Yucui G. New exact solutions to the Fitzhugh–Nagumo equation, Appl.
Math. Comput. 180, 524-528, 2006.