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

Year 2018, Volume: 10, 202 - 206, 29.12.2018

Abstract

In this article, the travelling wave solutions of the
medium equal width equation are obtained using the modified expansion method.
The solution functions were obtained by selecting the appropriate parameters.
It has been checked that these functions provide the MEW equation. Density, two
and three dimensional graphics of 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, topological and singular soliton properties.

References

  • Hossain, A. K. S., & Akbar, M. A., Closed form solutions of two nonlinear equation via the enhanced (G′/G)-expansion method. Cogent Mathematics & Statistics, (2017), 4(1), 1355958.
  • Eilbeck, J. C., & McGuire, G. R., Numerical study of the regularized long-wave equation. II: Interaction of solitary waves. Journal of Computational Physics, (1977), 23(1), 63-73.
  • Baskonus, H.M., Bulut, H., New hyperbolic function solutions for some nonlinear partial differential equation arising in mathematical physics. Entropy (2015), Vol. 17, 4255–4270.
  • 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, (2011), 235(14), 4003-4014.
  • Bulut, H., Sulaiman, T.A., Baskonus, H.M.: New solitary and optical wave structures to the Korteweg–deVries equation with dual-power law nonlinearity. Opt. Quant. Electron (2016),Vol. 48, 564.
  • R. Fetecau and D. Levy, “Approximate model equations for water waves,” Communications in Mathematical Sciences (2005), Vol. 3, No. 2, pp. 159–170.
  • 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, (2017) 132(11), 482.
  • He, J. H., & Wu, X. H. Exp-function method for nonlinear wave equations. Chaos, Solitons & Fractals, (2006) 30(3), 700-708.
  • Hossain, AKM Kazi Sazzad, and M. Ali Akbar. "Closed form solutions of two nonlinear equation via the enhanced (G′/G)-expansion method." Cogent Mathematics & Statistics 4.1 (2017): 1355958.
  • Naher, H., & Abdullah, F. A. New approach of (G′/G)-expansion method and new approach of generalized (G′/G)-expansion method for nonlinear evolution equation. AIP Advances (2013), 3(3), 032116.
Year 2018, Volume: 10, 202 - 206, 29.12.2018

Abstract

References

  • Hossain, A. K. S., & Akbar, M. A., Closed form solutions of two nonlinear equation via the enhanced (G′/G)-expansion method. Cogent Mathematics & Statistics, (2017), 4(1), 1355958.
  • Eilbeck, J. C., & McGuire, G. R., Numerical study of the regularized long-wave equation. II: Interaction of solitary waves. Journal of Computational Physics, (1977), 23(1), 63-73.
  • Baskonus, H.M., Bulut, H., New hyperbolic function solutions for some nonlinear partial differential equation arising in mathematical physics. Entropy (2015), Vol. 17, 4255–4270.
  • 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, (2011), 235(14), 4003-4014.
  • Bulut, H., Sulaiman, T.A., Baskonus, H.M.: New solitary and optical wave structures to the Korteweg–deVries equation with dual-power law nonlinearity. Opt. Quant. Electron (2016),Vol. 48, 564.
  • R. Fetecau and D. Levy, “Approximate model equations for water waves,” Communications in Mathematical Sciences (2005), Vol. 3, No. 2, pp. 159–170.
  • 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, (2017) 132(11), 482.
  • He, J. H., & Wu, X. H. Exp-function method for nonlinear wave equations. Chaos, Solitons & Fractals, (2006) 30(3), 700-708.
  • Hossain, AKM Kazi Sazzad, and M. Ali Akbar. "Closed form solutions of two nonlinear equation via the enhanced (G′/G)-expansion method." Cogent Mathematics & Statistics 4.1 (2017): 1355958.
  • Naher, H., & Abdullah, F. A. New approach of (G′/G)-expansion method and new approach of generalized (G′/G)-expansion method for nonlinear evolution equation. AIP Advances (2013), 3(3), 032116.
There are 10 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Tolga Aktürk

Hasan Bulut This is me

Gülnur Yel

Publication Date December 29, 2018
Published in Issue Year 2018 Volume: 10

Cite

APA Aktürk, T., Bulut, H., & Yel, G. (2018). An Application of the Modified Expansion Method to Nonlinear Partial Differential Equation. Turkish Journal of Mathematics and Computer Science, 10, 202-206.
AMA Aktürk T, Bulut H, Yel G. An Application of the Modified Expansion Method to Nonlinear Partial Differential Equation. TJMCS. December 2018;10:202-206.
Chicago Aktürk, Tolga, Hasan Bulut, and Gülnur Yel. “An Application of the Modified Expansion Method to Nonlinear Partial Differential Equation”. Turkish Journal of Mathematics and Computer Science 10, December (December 2018): 202-6.
EndNote Aktürk T, Bulut H, Yel G (December 1, 2018) An Application of the Modified Expansion Method to Nonlinear Partial Differential Equation. Turkish Journal of Mathematics and Computer Science 10 202–206.
IEEE T. Aktürk, H. Bulut, and G. Yel, “An Application of the Modified Expansion Method to Nonlinear Partial Differential Equation”, TJMCS, vol. 10, pp. 202–206, 2018.
ISNAD Aktürk, Tolga et al. “An Application of the Modified Expansion Method to Nonlinear Partial Differential Equation”. Turkish Journal of Mathematics and Computer Science 10 (December 2018), 202-206.
JAMA Aktürk T, Bulut H, Yel G. An Application of the Modified Expansion Method to Nonlinear Partial Differential Equation. TJMCS. 2018;10:202–206.
MLA Aktürk, Tolga et al. “An Application of the Modified Expansion Method to Nonlinear Partial Differential Equation”. Turkish Journal of Mathematics and Computer Science, vol. 10, 2018, pp. 202-6.
Vancouver Aktürk T, Bulut H, Yel G. An Application of the Modified Expansion Method to Nonlinear Partial Differential Equation. TJMCS. 2018;10:202-6.