An Application of the Modified Expansion Method to Nonlinear Partial Differential Equation

An Application of the Modified Expansion Method to Nonlinear Partial Differential Equation

In this article, the travelling wave solutions of the medium equal width equation are obtained usingthe modified expansion method. The solution functions were obtained by selecting the appropriate parameters. Ithas been checked that these functions provide the MEW equation. Density, two and three dimensional graphicsof the obtained solutions and other mathematical operations were found with the Mathematica software program.When the resulting solution functions are examined, it is determined that they include trigonometric, topologicaland singular soliton properties.

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  • [1] Hossain, A.K.S, Akbar, M.A., Closed form solutions of two nonlinear equation via the enhanced (G 0 /G) expansion method, Cogent Mathematics and Statistics, 4(2017), 1355958.
  • [2] Eilbeck,J.C.,McGuire, G.R., Numerical study of the regularized long-wave equation. II: Interaction of solitary waves,Journal of Computational Physics, 23(1977), 63-73.
  • [3] Baskonus, H.M., Bulut, H., New hyperbolic function solutions for some nonlinear partial differential equation arising in mathematical physics, Entropy, 17(2015), 4255-4270.
  • [4] Mohammadi, M., Mokhtari, R., Solving the generalized regularized long wave equation on the basis of a reproducing kernel space, Journal of Computational and Applied Mathematics, 235(2011), 4003-4014.
  • [5] Bulut, H., Sulaiman, T.A., Baskonus, H.M., New solitary and optical wave structures to the KortewegOC¸ ˆodeVries equation with dual-power ˆ law nonlinearity, Opt. Quant. Electron, 48(2016), 564.
  • [6] Fetecau,R., Levy,D., Approximate model equations for water waves, Communications in Mathematical Sciences, 3(2005), 159OC¸ o170.
  • [7] Baskonus, H.M., Bulut, H., Sulaiman, T. A. Investigation of various travelling wave solutions to the extended (2+1)-dimensional quantum ZK equation, The European Physical Journal Plus, 132(2017), 482. 1
  • [8] He, J.H., Wu, X.H.,Exp-function method for nonlinear wave equations , Chaos, Solitons and Fractals, 30(2006), 700-708. 1
  • [9] Kazi Sazzad Hossain, A.K.M., Ali Akbar, M., Closed form solutions of two nonlinear equation via the enhanced (G 0 /G) expansion method, Cogent Mathematics and Statistics, 4(2017), 1355958. 1
  • [10] Naher, H., Abdullah, F.A., New approach of (G 0 /G) -expansion method and new approach of generalized (G 0/G) - expansion method for nonlinear evolution equation, AIP Advances, 3(2013), 032116.