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ANALYTICAL SOLUTIONS OF (1+1)- DIMENSIONAL DISTRIBUTED LONG WAVE (DLW) EQUATION WITH AUXILIARY EQUATION METHOD

Year 2022, Volume: 5 Issue: 2, 88 - 94, 31.07.2022
https://doi.org/10.33773/jum.1089362

Abstract

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.

References

  • [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).
Year 2022, Volume: 5 Issue: 2, 88 - 94, 31.07.2022
https://doi.org/10.33773/jum.1089362

Abstract

References

  • [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).
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Ahmet Mücahid Göktaş 0000-0001-7237-8027

Koray Yılmaz 0000-0002-8641-0603

Orkun Taşbozan 0000-0001-5003-6341

Publication Date July 31, 2022
Submission Date March 17, 2022
Acceptance Date July 23, 2022
Published in Issue Year 2022 Volume: 5 Issue: 2

Cite

APA Göktaş, A. M., Yılmaz, K., & Taşbozan, O. (2022). ANALYTICAL SOLUTIONS OF (1+1)- DIMENSIONAL DISTRIBUTED LONG WAVE (DLW) EQUATION WITH AUXILIARY EQUATION METHOD. Journal of Universal Mathematics, 5(2), 88-94. https://doi.org/10.33773/jum.1089362
AMA Göktaş AM, Yılmaz K, Taşbozan O. ANALYTICAL SOLUTIONS OF (1+1)- DIMENSIONAL DISTRIBUTED LONG WAVE (DLW) EQUATION WITH AUXILIARY EQUATION METHOD. JUM. July 2022;5(2):88-94. doi:10.33773/jum.1089362
Chicago Göktaş, Ahmet Mücahid, Koray Yılmaz, and Orkun Taşbozan. “ANALYTICAL SOLUTIONS OF (1+1)- DIMENSIONAL DISTRIBUTED LONG WAVE (DLW) EQUATION WITH AUXILIARY EQUATION METHOD”. Journal of Universal Mathematics 5, no. 2 (July 2022): 88-94. https://doi.org/10.33773/jum.1089362.
EndNote Göktaş AM, Yılmaz K, Taşbozan O (July 1, 2022) ANALYTICAL SOLUTIONS OF (1+1)- DIMENSIONAL DISTRIBUTED LONG WAVE (DLW) EQUATION WITH AUXILIARY EQUATION METHOD. Journal of Universal Mathematics 5 2 88–94.
IEEE A. M. Göktaş, K. Yılmaz, and O. Taşbozan, “ANALYTICAL SOLUTIONS OF (1+1)- DIMENSIONAL DISTRIBUTED LONG WAVE (DLW) EQUATION WITH AUXILIARY EQUATION METHOD”, JUM, vol. 5, no. 2, pp. 88–94, 2022, doi: 10.33773/jum.1089362.
ISNAD Göktaş, Ahmet Mücahid et al. “ANALYTICAL SOLUTIONS OF (1+1)- DIMENSIONAL DISTRIBUTED LONG WAVE (DLW) EQUATION WITH AUXILIARY EQUATION METHOD”. Journal of Universal Mathematics 5/2 (July 2022), 88-94. https://doi.org/10.33773/jum.1089362.
JAMA Göktaş AM, Yılmaz K, Taşbozan O. ANALYTICAL SOLUTIONS OF (1+1)- DIMENSIONAL DISTRIBUTED LONG WAVE (DLW) EQUATION WITH AUXILIARY EQUATION METHOD. JUM. 2022;5:88–94.
MLA Göktaş, Ahmet Mücahid et al. “ANALYTICAL SOLUTIONS OF (1+1)- DIMENSIONAL DISTRIBUTED LONG WAVE (DLW) EQUATION WITH AUXILIARY EQUATION METHOD”. Journal of Universal Mathematics, vol. 5, no. 2, 2022, pp. 88-94, doi:10.33773/jum.1089362.
Vancouver Göktaş AM, Yılmaz K, Taşbozan O. ANALYTICAL SOLUTIONS OF (1+1)- DIMENSIONAL DISTRIBUTED LONG WAVE (DLW) EQUATION WITH AUXILIARY EQUATION METHOD. JUM. 2022;5(2):88-94.