Araştırma Makalesi
ANALYTICAL SOLUTIONS OF (1+1)- DIMENSIONAL DISTRIBUTED LONG WAVE (DLW) EQUATION WITH AUXILIARY EQUATION METHOD
Öz
In this article, the exact solutions of the (1+1)-dimensional (DLW) equation, a fractional partial differential equation in conformable sense, which is a nonlinear, are given. Furthermore, with the aid of the mathematica program it is seen that the analytical solutions revealed with the auxiliary equation method satisfies the equation.
Anahtar Kelimeler
(1 + 1)-Dimensional Distributed Long Wave Equation Auxiliary Equation Method Conformable Differential Equations
Kaynakça
- [1] S. Abbasbandy, The application of homotopy analysis method to nonlinear equations arising in heat transfer, Physics Letters A, 360(1), pp. 109-113 (2006).
- [2] M.A. Abdou, A generalized auxiliary equation method and its applications, Nonlinear Dynamics, 52(1), pp. 95-102 (2008).
- [3] M.A. Abdou, Further improved F-expansion and new exact solutions for nonlinear evolution equations, Nonlinear Dynamics, 52(3), pp. 227-288 (2008).
- [4] L.A. Alhakim and A.A. Moussa, The double auxiliary equations method and its application to space-time fractional nonlinear equations,Journal of Ocean Engineering and Science, 4, pp. 7-13 (2019).
- [5] G. Cai, Q. Wang and J. Huang, A modified F-expansion method for solving breaking soliton equation, Int J Nonlinear Sci, 2(2), 122-128 (2006).
- [6] Y. Chen and Z. Yan, The Weierstrass elliptic function expansion method and its applications in nonlinear wave equations, Chaos Solitons Fractals, 29(4), 948964 (2006).
- [7] Y. Gurefe, A. Sonmezoglu and E. Misirli, Application of trial equation method to the nonlinear partial differential equations arising in mathematical physics, Pramana J Phys, 77(6), 1023-1029 (2011).
- [8] Y. Gurefe, E. Misirli, A. Sonmezoglu and M. Ekici, Extended trial equation method to generalized nonlinear partial differential equations, Appl Math Comput, 219(10), 52535260 (2013).
- [9] S. Jiong and Sirendaoreji, Auxiliary equation method for solving nonlinear partial differential equations, Physics Letters A, 309(5-6), 387-396 (2003).
- [10] R. Khalil, M. Horani, A. Yousef. and M. Sababheh, A new definition of fractional derivative, Journal of Computational and Applied Mathematics, 264, 65-70 (2014).
- [11] W. Maliet and W. Hereman, The Tanh Method: Exact Solutions of Nonlinear Evolution and Wave Equations, Physica Scripta, 54(6), 563-568 (1996).
- [12] O. Tasbozan, A. Kurt and A. Tozar, New optical solutions of complex GinzburgLandau equation arising in semiconductor lasers, Applied Physics B, 125(6), 104 (2019).
- [13] S. Zhang and T. Xia, A generalized F-expansion method with symbolic computation exactly solving BroerKaup equations, Appl Math Comput, 189(1), 949-955 (2007).
- [14] S. Ylmaz, Yardmc Denklem Yntemi Yardm le Baz Kesirli Mertebeden Ksmi Diferansiyel Denklemlerin Analitik zmler. M.Sc. Thesis. Hatay Mustafa Kemal niversitesi, (2019).
Yıl 2022,
Cilt: 5 Sayı: 2, 88 - 94, 31.07.2022
Öz
Kaynakça
- [1] S. Abbasbandy, The application of homotopy analysis method to nonlinear equations arising in heat transfer, Physics Letters A, 360(1), pp. 109-113 (2006).
- [2] M.A. Abdou, A generalized auxiliary equation method and its applications, Nonlinear Dynamics, 52(1), pp. 95-102 (2008).
- [3] M.A. Abdou, Further improved F-expansion and new exact solutions for nonlinear evolution equations, Nonlinear Dynamics, 52(3), pp. 227-288 (2008).
- [4] L.A. Alhakim and A.A. Moussa, The double auxiliary equations method and its application to space-time fractional nonlinear equations,Journal of Ocean Engineering and Science, 4, pp. 7-13 (2019).
- [5] G. Cai, Q. Wang and J. Huang, A modified F-expansion method for solving breaking soliton equation, Int J Nonlinear Sci, 2(2), 122-128 (2006).
- [6] Y. Chen and Z. Yan, The Weierstrass elliptic function expansion method and its applications in nonlinear wave equations, Chaos Solitons Fractals, 29(4), 948964 (2006).
- [7] Y. Gurefe, A. Sonmezoglu and E. Misirli, Application of trial equation method to the nonlinear partial differential equations arising in mathematical physics, Pramana J Phys, 77(6), 1023-1029 (2011).
- [8] Y. Gurefe, E. Misirli, A. Sonmezoglu and M. Ekici, Extended trial equation method to generalized nonlinear partial differential equations, Appl Math Comput, 219(10), 52535260 (2013).
- [9] S. Jiong and Sirendaoreji, Auxiliary equation method for solving nonlinear partial differential equations, Physics Letters A, 309(5-6), 387-396 (2003).
- [10] R. Khalil, M. Horani, A. Yousef. and M. Sababheh, A new definition of fractional derivative, Journal of Computational and Applied Mathematics, 264, 65-70 (2014).
- [11] W. Maliet and W. Hereman, The Tanh Method: Exact Solutions of Nonlinear Evolution and Wave Equations, Physica Scripta, 54(6), 563-568 (1996).
- [12] O. Tasbozan, A. Kurt and A. Tozar, New optical solutions of complex GinzburgLandau equation arising in semiconductor lasers, Applied Physics B, 125(6), 104 (2019).
- [13] S. Zhang and T. Xia, A generalized F-expansion method with symbolic computation exactly solving BroerKaup equations, Appl Math Comput, 189(1), 949-955 (2007).
- [14] S. Ylmaz, Yardmc Denklem Yntemi Yardm le Baz Kesirli Mertebeden Ksmi Diferansiyel Denklemlerin Analitik zmler. M.Sc. Thesis. Hatay Mustafa Kemal niversitesi, (2019).
Toplam 14 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Temmuz 2022 |
| Gönderilme Tarihi | 17 Mart 2022 |
| Kabul Tarihi | 23 Temmuz 2022 |
| Yayımlandığı Sayı | Yıl 2022 Cilt: 5 Sayı: 2 |
