Analytical studies on the (1 + 1)-dimensional nonlinear Dispersive Modified Benjamin–Bona–Mahony equation defined by seismic sea waves

References

• Chunga K, Toulkeridis T. First evidence of aleo-tsunami deposits of a major historic event in Ecuador. J. Tsunami Soc. Int. 2014;33:55–69.
   Google Scholar
• Yusufoğlu E. New solitonary solutions for the MBBM equations using exp-function method. Phys. Lett. A. 2008;372:442–446.10.1016/j.physleta.2007.07.062
   Web of Science ®Google Scholar
• Zayed EME, Al-Joudi S. Applications of an extended (G′/G)-expansion method to find exact solutions of nonlinear PDEs in mathematical physics. Math. Prob. Eng. 2010;2010:19. doi:10.1155/2010/768573.
   Web of Science ®Google Scholar
• Hafez MG, Alam MN, Akbar MA. Travelling wave solutions for some important coupled nonlinear physical models via the coupled Higgs equation and the Maccari system. J. King Saud Univ. – Sci. 2015;27:105–112.
   Google Scholar
• Liu CS. Trial equation method and its applications to nonlinear evolution equations. Acta Phys. Sin. 2005;54:2505–2509.
   Web of Science ®Google Scholar
• Liu CS. A new trial equation method and its applications. Commun. Theor. Phys. 2006;45:395–397.
   Web of Science ®Google Scholar
• Liu CS. Trial equation method for nonlinear evolution equations with rank inhomogeneous: mathematical discussions and applications. Commun. Theor. Phys. 2006;45:219–223.
   Web of Science ®Google Scholar
• Baskonus HM, Bulut H, Belgacem FBM. On some new exact solutions of special type of the nonlinear Dodd–Bullough–Mikhailov equation. 3rd International Conference on Mathematical, Computational and Statistical Sciences (MCSS’15); 2015 February 22–24; Dubai, United Arab Emirates. p. 76–85.
   Google Scholar
• Zayed EME, Abdelaziz MAM. Exact solutions for the nonlinear Schrödinger equation with variable coefficients using the generalized extended tanh-function, the sine–cosine and the exp-function methods. Appl. Math. Comput. 2011;218:2259–2268.10.1016/j.amc.2011.07.043
   Web of Science ®Google Scholar
• Wazwaz AM. The tanh method: solitons and periodic solutions for the Dodd–Bullough–Mikhailov and the Tzitzeica–Dodd–Bullough equations. Chaos, Solitons Fractals. 2005;25:55–63.10.1016/j.chaos.2004.09.122
   Web of Science ®Google Scholar
• Khan K, Akbar MA. Traveling wave solutions of the (2 + 1)-dimensional Zoomeron equation and the Burgers equations via the MSE method and the Exp-function method. Ain Shams Eng. J. 2014;5:247–256.10.1016/j.asej.2013.07.007
   Google Scholar
• Khan K, Akbar MA, Rayhanul Islam SM. Exact solutions for (1 + 1)-dimensional nonlinear dispersive modified Benjamin–Bona–Mahony equation and coupled Klein–Gordon equations. SpringerPlus. 2014;3:19 p.
   PubMedGoogle Scholar
• Khan K, Akbar MA. Exact solutions of the (2 + 1)-dimensional cubic Klein–Gordon equation and the (3 + 1)-dimensional Zakharov–Kuznetsov equation using the modified simple equation method. J. Assoc. Arab Univ. Basic Appl. Sci. 2014;15:74–81.10.1016/j.jaubas.2013.05.001
   Google Scholar
• Naher H, Abdullah FA, Bekir A. Some new traveling wave solutions of the modified Benjamin–Bona–Mahony equation via the improved (G′/G)-expansion method. New Trends Math. Sci. 2015;3:78–89.
   Google Scholar
• He JH, Wu XH. Exp-function method for nonlinear wave equations. Chaos, Solitons Fractals. 2006;30:700–708.10.1016/j.chaos.2006.03.020
   Web of Science ®Google Scholar
• Wu XH, He JH. Solitary solutions, periodic solutions and compacton-like solutions using the exp-function method. Comput. Math. Appl. 2007;54:966–986.
   Web of Science ®Google Scholar
• He JH. An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering. Int. J. Mod. Phys. B. 2008;22:3487–3578.10.1142/S0217979208048668
   Web of Science ®Google Scholar
• He JH. Some asymptotic methods for strongly nonlinear equations. Int. J. Mod. Phys. B. 2006;20:1141–1199.10.1142/S0217979206033796
   Web of Science ®Google Scholar
• Moradi E, Varasteh H, Abdollahzadeh A, Mostafaei-Malekshah M. The exp-function method for solving two dimensional sine-Bratu type equations. Appl. Math. 2014;5:1212–1217.10.4236/am.2014.58112
   Google Scholar
• Bekir A, Boz A. Exact solutions for nonlinear evolution equations using Exp-function method. Phys. Lett. A. 2008;372:1619–1625.10.1016/j.physleta.2007.10.018
   Web of Science ®Google Scholar
• Ebaid A. Exact solitary wave solutions for some nonlinear evolution equations via exp-function method. Phys. Lett. A. 2007;365:213–219.10.1016/j.physleta.2007.01.009
   Web of Science ®Google Scholar
• Abdou MA, Soliman AA, El-Basyony ST. New application of Exp-function method for improved Boussinesq equation. Phys. Lett. A. 2007;369:469–475.10.1016/j.physleta.2007.05.039
   Web of Science ®Google Scholar
• Uddin S, Alam N, Hossain SMS, Samiu H, Akbar MA. Some new exact traveling wave solutions to the (3 + 1)-dimensional Zakharov–Kuznetsov equation and the Burgers equations via Exp (−ϕ)-expansion method. Front. Math. Appl. 2014;1:1–8.
   Google Scholar