Research Article
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Year 2017, Volume: 2 Issue: 1, 13 - 26, 30.04.2017

Yusuf Pandir Halime Ulusoy

https://doi.org/10.30931/jetas.303875

Abstract

References

  • [1] A. Biswas, H. Triki, 1-Soliton solution of the D(m; n) equation with generalized evolution, Appl. Math. Comput. 217 (2011), 8482-8488.
  • [2] R. Hirota, Exact solution of the KdV equation for multiple collisions of solitons, Phys. Rev. Lett. 27 (1971), 1192-1194.
  • [3] R. Hirota, Exact N-soliton solution of the wave equation of long waves in shallow and nonlinear lattices, J. Math. Phys. 14 (1973), 810-814.
  • [4] Y. Gurefe, E. Misirli, Exp-function method for solving nonlinear evolution equations with higher order nonlinearity, Comput. Math. Appl. 61 (2011), 2025-2030.
  • [5] E. Misirli, Y. Gurefe, Exp-function method for solving nonlinear evolution equations, Math. Comput. Appl. 16 (2011), 258-266.
  • [6] Y. Gurefe, E. Misirli, New variable separation solutions of two-dimensional Burgers system, Appl. Math. Comput. 217 (2011), 9189-9197.
  • [7] Y. Gurefe, A. Sonmezoglu, E. Misirli, Application of the trial equation method for solving some nonlinear evolution equations arising in mathematical physics, Pramana-J. Phys. 77 (2011), 1023-1029.
  • [8] Z.D. Dai, C.J. Wang, S.Q. Lin, D.L. Li, G. Mu, The three-wave method for nonlinear evolution equations, Nonl. Sci. Lett. A. 1 (2010), 77-82.
  • [9] Y. Shi, Z.D. Dai, S. Han, L. Huang, The multi-wave method for nonlinear evolution equations, Math. Comput. Appl. 15 (2010), 776-783.
  • [10] Y. Shi, D. Li, New exact solutions for the (2+1)-dimensional SawadaKotera equation, Comput. Fluids 68 (2012), 88-93.
  • [11] Y. Gurefe, Y. Pandir, E. Misirli, New Exact Solutions of Stochastic KdV Equation, Appl. Math. Sci. 6(65) (2012) 3225-3234.
  • [12] L. Girgis, A. Biswas, Soliton perturbation theory for nonlinear wave equations, Appl. Math. Comput. 216 (2010), 2226-2231.
  • [13] A. Biswas, S. Konar, Soliton perturbation theory for the fth order KdV-type equations with power law nonlinearity, Appl. Math. Lett. 20 (2007), 1122-1125.

The Multi-Wave Method for Exact Solutions of Nonlinear Partial Differential Equations

Year 2017, Volume: 2 Issue: 1, 13 - 26, 30.04.2017

Yusuf Pandir Halime Ulusoy

https://doi.org/10.30931/jetas.303875

Abstract

In this research, we use the multi-wave method to obtain new exact solutions for generalized forms of 5th order KdV equation and fth order KdV (fKdV) equation with power law nonlinearity. Computations are performed with the help of the mathematics software Mathematica. Then, periodic wave solutions, bright soliton solutions and rational function solutions with free parameters are obtained by this approach. It is shown that this method is very useful and effective.

Keywords

Multi-wave method generalized forms of 5th order KdV equation fth order KdV (fKdV) equation Soliton solutions.

References

  • [1] A. Biswas, H. Triki, 1-Soliton solution of the D(m; n) equation with generalized evolution, Appl. Math. Comput. 217 (2011), 8482-8488.
  • [2] R. Hirota, Exact solution of the KdV equation for multiple collisions of solitons, Phys. Rev. Lett. 27 (1971), 1192-1194.
  • [3] R. Hirota, Exact N-soliton solution of the wave equation of long waves in shallow and nonlinear lattices, J. Math. Phys. 14 (1973), 810-814.
  • [4] Y. Gurefe, E. Misirli, Exp-function method for solving nonlinear evolution equations with higher order nonlinearity, Comput. Math. Appl. 61 (2011), 2025-2030.
  • [5] E. Misirli, Y. Gurefe, Exp-function method for solving nonlinear evolution equations, Math. Comput. Appl. 16 (2011), 258-266.
  • [6] Y. Gurefe, E. Misirli, New variable separation solutions of two-dimensional Burgers system, Appl. Math. Comput. 217 (2011), 9189-9197.
  • [7] Y. Gurefe, A. Sonmezoglu, E. Misirli, Application of the trial equation method for solving some nonlinear evolution equations arising in mathematical physics, Pramana-J. Phys. 77 (2011), 1023-1029.
  • [8] Z.D. Dai, C.J. Wang, S.Q. Lin, D.L. Li, G. Mu, The three-wave method for nonlinear evolution equations, Nonl. Sci. Lett. A. 1 (2010), 77-82.
  • [9] Y. Shi, Z.D. Dai, S. Han, L. Huang, The multi-wave method for nonlinear evolution equations, Math. Comput. Appl. 15 (2010), 776-783.
  • [10] Y. Shi, D. Li, New exact solutions for the (2+1)-dimensional SawadaKotera equation, Comput. Fluids 68 (2012), 88-93.
  • [11] Y. Gurefe, Y. Pandir, E. Misirli, New Exact Solutions of Stochastic KdV Equation, Appl. Math. Sci. 6(65) (2012) 3225-3234.
  • [12] L. Girgis, A. Biswas, Soliton perturbation theory for nonlinear wave equations, Appl. Math. Comput. 216 (2010), 2226-2231.
  • [13] A. Biswas, S. Konar, Soliton perturbation theory for the fth order KdV-type equations with power law nonlinearity, Appl. Math. Lett. 20 (2007), 1122-1125.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Yusuf Pandir

Halime Ulusoy This is me

Publication Date April 30, 2017
Published in Issue Year 2017 Volume: 2 Issue: 1

Cite

APA Pandir, Y., & Ulusoy, H. (2017). The Multi-Wave Method for Exact Solutions of Nonlinear Partial Differential Equations. Journal of Engineering Technology and Applied Sciences, 2(1), 13-26. https://doi.org/10.30931/jetas.303875
AMA Pandir Y, Ulusoy H. The Multi-Wave Method for Exact Solutions of Nonlinear Partial Differential Equations. JETAS. April 2017;2(1):13-26. doi:10.30931/jetas.303875
Chicago Pandir, Yusuf, and Halime Ulusoy. “The Multi-Wave Method for Exact Solutions of Nonlinear Partial Differential Equations”. Journal of Engineering Technology and Applied Sciences 2, no. 1 (April 2017): 13-26. https://doi.org/10.30931/jetas.303875.
EndNote Pandir Y, Ulusoy H (April 1, 2017) The Multi-Wave Method for Exact Solutions of Nonlinear Partial Differential Equations. Journal of Engineering Technology and Applied Sciences 2 1 13–26.
IEEE Y. Pandir and H. Ulusoy, “The Multi-Wave Method for Exact Solutions of Nonlinear Partial Differential Equations”, JETAS, vol. 2, no. 1, pp. 13–26, 2017, doi: 10.30931/jetas.303875.
ISNAD Pandir, Yusuf - Ulusoy, Halime. “The Multi-Wave Method for Exact Solutions of Nonlinear Partial Differential Equations”. Journal of Engineering Technology and Applied Sciences 2/1 (April 2017), 13-26. https://doi.org/10.30931/jetas.303875.
JAMA Pandir Y, Ulusoy H. The Multi-Wave Method for Exact Solutions of Nonlinear Partial Differential Equations. JETAS. 2017;2:13–26.
MLA Pandir, Yusuf and Halime Ulusoy. “The Multi-Wave Method for Exact Solutions of Nonlinear Partial Differential Equations”. Journal of Engineering Technology and Applied Sciences, vol. 2, no. 1, 2017, pp. 13-26, doi:10.30931/jetas.303875.
Vancouver Pandir Y, Ulusoy H. The Multi-Wave Method for Exact Solutions of Nonlinear Partial Differential Equations. JETAS. 2017;2(1):13-26.