Öz
Bu
çalışmada, geliştirilmiş Bernoulli fonksiyon yönteminin Drinfeld-Sokolov
sistemine uygulanması sunulmuştur. Literatürdeki diğer makalelerden faklı yeni
çözümler bulduk. Ek olarak, bu makaledeki tüm hesaplamalar ve grafik çizimleri
Wolfram Mathematica 9 programı yardımıyla yapılmıştır.
Anahtar Kelimeler
Geliştirilmiş Bernoulli Denklem Metodu Drinfeld-Sokolov denklemi
Kaynakça
- [1] Goktas U., Hereman W. Symbolic computation of conserved densities for systems of nonlinear evolution equations. Journal of Symbolic Computation. 24:5, 591-621, 1997. [2] Olver P.J. Applications of Lie Groups to Differential Equations, vol. 107 of Graduate Texts in Mathematics, Springer, New York, USA, 2nd edition. 1993. [3] Wang J.P. A list of 1 + 1 dimensional integrable equations and their properties. Journal of Nonlinear Mathematical Physics, 9:1, 213-233, 2002. [4] Baskonus H.M., Bulut H. On the complex structures of Kundu-Eckhaus equation via improved Bernoulli sub-equation function method, Waves in Randomand Complex Media. 25(4) 720-728. 2015 [5] Wazwaz A.M. Exact and explicit travelling wave solutions for the nonlinear Drinfeld-Sokolov system. Communications in Nonlinear Science and Numerical Simulation. 11:3, 311-325, 2006. [6] El-Wakil S.A. Abdou M.A. Modified extended tanhfunction method for solving nonlinear partial differential equations. Chaos, Solitons Fractals, 31:5, 1256-1264, 2007. [7] Zhang F., Qi J., Yuan W. Modified extended tanhfunction method for solving nonlinear partial differential equations,” Journal of Applied Mathematics, 2013:2013. [8] Zheng B. A new Bernoulli sub-ODE method for constructing traveling wave solutions for two nonlinear equations with any order, U. P. B. Sci. Bull., Series A. 73:3, 2011. [9] Zheng B. Application of A Generalized Bernoulli Sub-ODE Method For Finding Traveling Solutions of Some Nonlinear Equations, WSEAS Transactions on Mathematics, 7:11, 618-626, 2012. [10] Baskonus H.M. Koc D.A. Bulut H. New travelling wave prototypes to the nonlinear Zakharov-Kuznetsov equation with power law nonlinearity, Nonlinear Sci. Lett. A, 7:2, 67-76, 2016.
Öz
In
this study, the Drinfeld-Sokolov system is solved by the application of the
improved Bernoulli sub-equation function method (IBSEFM). We have found new
solutions different from the others articles in the literature. In addition, we
carried all the computations out and the graphics plot in this article by software
Wolfram Mathematica 9.
Anahtar Kelimeler
Improved Bernoulli sub-equation function method Drinfeld-Sokolov equations
Kaynakça
- [1] Goktas U., Hereman W. Symbolic computation of conserved densities for systems of nonlinear evolution equations. Journal of Symbolic Computation. 24:5, 591-621, 1997. [2] Olver P.J. Applications of Lie Groups to Differential Equations, vol. 107 of Graduate Texts in Mathematics, Springer, New York, USA, 2nd edition. 1993. [3] Wang J.P. A list of 1 + 1 dimensional integrable equations and their properties. Journal of Nonlinear Mathematical Physics, 9:1, 213-233, 2002. [4] Baskonus H.M., Bulut H. On the complex structures of Kundu-Eckhaus equation via improved Bernoulli sub-equation function method, Waves in Randomand Complex Media. 25(4) 720-728. 2015 [5] Wazwaz A.M. Exact and explicit travelling wave solutions for the nonlinear Drinfeld-Sokolov system. Communications in Nonlinear Science and Numerical Simulation. 11:3, 311-325, 2006. [6] El-Wakil S.A. Abdou M.A. Modified extended tanhfunction method for solving nonlinear partial differential equations. Chaos, Solitons Fractals, 31:5, 1256-1264, 2007. [7] Zhang F., Qi J., Yuan W. Modified extended tanhfunction method for solving nonlinear partial differential equations,” Journal of Applied Mathematics, 2013:2013. [8] Zheng B. A new Bernoulli sub-ODE method for constructing traveling wave solutions for two nonlinear equations with any order, U. P. B. Sci. Bull., Series A. 73:3, 2011. [9] Zheng B. Application of A Generalized Bernoulli Sub-ODE Method For Finding Traveling Solutions of Some Nonlinear Equations, WSEAS Transactions on Mathematics, 7:11, 618-626, 2012. [10] Baskonus H.M. Koc D.A. Bulut H. New travelling wave prototypes to the nonlinear Zakharov-Kuznetsov equation with power law nonlinearity, Nonlinear Sci. Lett. A, 7:2, 67-76, 2016.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 28 Haziran 2018 |
| Yayımlandığı Sayı | Yıl 2018 Cilt: 6 Sayı: 1 |
