







Vol.2 , No. 6, Publication Date: Oct. 17, 2017, Page: 49-54
[1] | Muhammad Hashim, Department of Mathematics, National College of Business Administration & Economics, Gujrat, Pakistan. |
[2] | Madiha Afzal, Department of Mathematics, Allama Iqbal Open University, Islamabad, Pakistan. |
[3] | Qazi Mahmood Ul-Hassan, Department of Mathematics, University of Wah, Wah Cantt., Pakistan. |
[4] | Kamran Ayub, Department of Mathematics, Riphah International University, Islamabad, Pakistan. |
[5] | Faiza Yasmeen, Department of Mathematics, University of Wah, Wah Cantt., Pakistan. |
In this paper, the exp-function method has been used to find the soliton solutions of Fornberg-Whitham equation. The solution procedure of this method, with the help of symbolic computation of maple software, is of utter simplicity. The exp-function method is a powerful and straightforward mathematical tool to solve the nonlinear equations in mathematical physics.
Keywords
Exp-function Method, Fornberg-Whitham Equation, Soliton Solutions
Reference
[01] | J. H. He, Variational iteration method-a kind of non-linear analytical technique: some examples, Internat. J. Non-Linear Mech. 34 (4) (1999) 699–708. |
[02] | J. M. Burgers, A mathematical model illustrating the theory of turbulence, Adv. Appl. Mech. 1 (1948): 171-199. |
[03] | M. A. Noor, S. T Mohyud-Din, & A. Waheed, (2012). New soliton and periodic wave solutions of generalized Burgers-Huxley equation. Int. J. Mod. Phys. B. |
[04] | M. A. Noor, S. T Mohyud-Din, & A. Waheed, (2012). Exp-function method for generalized traveling solutions of the Lax equation. Int. J. Mod. Phys. B. |
[05] | M. A. Noor, S. T Mohyud-Din, & A. Waheed, (2012). Exp-function method for soliton solution of Reaction Diffusion equation. Int. J. Mod. Phys. B. |
[06] | J. H. He and M. A. Abdou, New periodic solutions for nonlinear evolution equation using exp-method, Chaos, Solitons & Fractals, 34 (2007): 1421-1429. |
[07] | W. Hereman and A. Nuseir, Symbolic methods to construct exact solutions of nonlinear partial differential equations, Math. Comput. Simulation, 43 (1997): 13–27. |
[08] | R. Hirota, The Direct Method in Soliton Theory, Cambridge University Press, Cambridge, 2004. |
[09] | R. M. Miura, The Korteweg de-Vries equation: a survey of results, SIAM Rev., 18 (1976): 412- 459. |
[10] | W. X. Ma, Complexiton solutions to the Korteweg-de Vries equation, Phys. Lett. A, 301 (2002): 35-44. |
[11] | W. X. Ma and B. Fuchssteiner, Explicit and exact solutions of Kolmogorov-PetrovskII-Piskunov equation, Int. J. Nonlin. Mech. 31 (3) (1996): 329-338. |
[12] | W. X. Ma and Y. You, Solving the Korteweg-de Vries equation by its bilinear form: Wronskian solutions, Transactions of the American Mathematical Society, 357 (2004): 1753-1778. |
[13] | W. X. Ma and Y. You, Rational solutions of the Toda lattice equation in Casoratian form, Chaos, Solitons & Fractals, 22 (2004): 395-406. |
[14] | W. X. Ma, H. Y. Wu and J. S. He, Partial differential equations possessing Frobenius integrable decompositions, Phys. Lett. A, 364 (2007): 29-32. |
[15] | F. Tascan, A. Bekir and M. Kopran, Traveling wave solutions of nonlinear evolution equation by using the first-integral method, Commun. Nonlin. Sci. Num. Sim. (2008), doi 10.1016/j.cnsns.2008.07.009. |
[16] | S. T. Mohyud-Din, M. A. Noor and K. I. Noor, Some relatively new techniques for nonlinear problems, Mathematical Problems in Engineering, Hindawi, 2009 (2009); Article ID 234849, 25 pages, doi: 10.1155/2009/234849. |
[17] | S. T. Mohyud-Din, Solution of nonlinear differential equations by exp-function method, World Applied Sciences Journal, 7 (2009): 116-147. |
[18] | M. A. Noor, S. T. Mohyud-Din and A. Waheed, Exp-function method for solving Kuramoto-Sivashinsky and Boussinesq equations, J. Appl. Math. Computg. (2008), doi: 10.1007/s12190-008-0083-y. |
[19] | S. T. Mohyud-Din, M. A. Noor and A. Waheed, Exp-function method for generalized travelling solutions of Calogero-Degasperis-Fokas equation, ZeitschriftfürNaturforschung A- A Journal of Physical Sciences, 65a (2010): 78-84. |
[20] | A. M. Wazwaz, The extended tanh method for Zakharov-Kuznetsov equation (ZK), the modified ZK equation and its generalized forms, Commun. Nonlin. Sci. Num. Sim. 13 (2008): 1039. |
[21] | J. H. He and X. H. Wu, Exp-function method for nonlinear wave equations, Chaos, Solitons & Fractals, 30 (3) (2006): 700–708. |
[22] | X. H. Wu and J. H. He, Solitary solutions, periodic solutions and compacton like solutions using the exp-function method, Comput. Math. Appl. 54 (2007): 966-986. |
[23] | E. Yusufoglu, New solitonary solutions for the MBBN equations using exp-function method, Phys. Lett. A. 372 (2008): 442-446. |
[24] | X. W. Zhou, Y. X. Wen and J. H. He, Exp-function method to solve the nonlinear dispersive k(m, n) equations, Int. J. Nonlin. Sci. Num. Sim. 9 (3) (2008): 301-306. |
[25] | S. Zhang, Application of exp-function method to high-dimensional nonlinear evolution equation, Chaos, Solitons &Fractals. 365 (2007): 448-455. |
[26] | S. D. Zhu, Exp-function method for the Hybrid-Lattice system, Inter. J. Nonlin. Sci. Numer. Sim. 8 (2007): 461-464. |
[27] | H. M. Fu, Z. D. Dai, Double exp-function method and application, Int. J. Nonlinear Sci. Numer. Simul. 10 (2009) 927–933. |
[28] | Z. D. Dai, C. J. Wang, S. Q. Lin, D. L. Li, G. Mu, The Three-wave method for nonlinear evolution equations, Nonlinear Sci. Lett. A: Math. Phys. Mech. 1 (1) (2010) 77–82. |
[29] | A. Wazwaz, Exact and explicit traveling wave solutions for the nonlinear Drinfel’d– Sokolov system, Commun. Nonlinear Sci. Numer. Simul. 11 (2006) 311–325. |
[30] | E. Sweet, R. A. V. Gorder, Analytical solutions to a generalized Drinfel’d–Sokolov equation related to DSSH and KdV6, Appl. Math. Comput. 216 (10) (2010) 2783–2791. |
[31] | B. Lia, Y. Chena, H. Zhanga, Auto-Backlund transformations and exact solutions for the generalized two-dimensional Korteweg–de Vries–Burgers-type equations and Burgers-type equations, Z. Naturforsch. 58a (2003) 464–472. |
[32] | W. X. Ma and E. G. Fan, Linear superposition principle applying to Hirota bilinear equations, Computers and Mathematics with Applications, 61 (2011): 950–959. |
[33] | W. X. Ma, Y. Zhang, Y. N. Tang and J. Y. Tu, Hirota bilinear equations with linear subspaces of solutions, Applied Mathematics and Computation, 218 (2012): 7174-7183. |