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Akışkanlar Mekaniğinde Doğrusal Olmayan Dalga Çözümlerinin İncelenmesi

Year 2021, , 168 - 173, 31.12.2021
https://doi.org/10.46810/tdfd.932252

Abstract

Bu çalışmada, (3 + 1) boyutlu potansiyel Yu-Toda-Sasa-Fukuyama (YTSF) denkleminin hareketli dalga çözümleri, modifiye üstel fonksiyon yöntemi (MEFM) kullanılarak elde edilmiştir. Bulunan çözüm fonksiyonları incelendiğinde trigonometrik, hiperbolik ve rasyonel fonksiyonların olduğu görülmektedir. Elde edilen çözüm fonksiyonları, (3 + 1) boyutlu potansiyel Yu-Toda-Sasa-Fukuyama (YTSF) denklemini sağlayan Wolfram Mathematica yazılımı ile kontrol edildi. Uygun parametreler belirlenerek çözüm fonksiyonunun iki ve üç boyutlu ve kontur grafikleri bulundu.

References

  • [1] Yang XF, Deng ZC, Wei YA. Riccati-Bernoulli sub-ODE method for nonlinear partial differential equations and its application. Advances in Difference equations. 2015; (1): 1-17.
  • [2] Baskonus HM, Bulut H. Exponential prototype structures for (2+1)-dimensional Boiti-Leon-Pempinelli systems in mathematical physics. Waves in Random and Complex Media. 2016; 26(2):189-196.
  • [3] Liu CS. Trial equation method and its applications to nonlinear evolution equations. Acta Physica Sinica. 2005; 54(6): 2505-2509.
  • [4] Liu CS. Trial equation method to nonlinear evolution equations with rank inhomogeneous: mathematical discussions and its applications. CoTPh. 2006; 45(2): 219-223.
  • [5] Abdelrahman MA. A note on Riccati-Bernoulli Sub-ODE method combined with complex transform method applied to fractional differential equations. Nonlinear Engineering. 2018; 7(4): 279-285.
  • [6] Bulut H, Baskonus HM and Pandir Y. The modified trial equation method for fractional wave equation and time fractional generalized Burgers equation. In Abstract and Applied Analysis Hindawi. 2013; Vol. 2013.
  • [7] Gurefe Y, Misirli E, Sonmezoglu A and Ekici M. Extended trial equation method to generalized nonlinear partial differential equations. Applied Mathematics and Computation. 2013; 219(10): 5253-5260.
  • [8] Elwakil SA, El-Labany SK, Zahran MA and Sabry R. Modified extended tanh-function method for solving nonlinear partial differential equations. Physics Letters A. 2002; 299(2-3): 179-188.
  • [9] Fan E and Hon YC. Applications of extended tanh method to ‘special’types of nonlinear equations. Applied Mathematics and Computation. 2003; 141(2-3): 351-358.
  • [10] Hosseini K and Gholamin P. Feng’s first integral method for analytic treatment of two higher dimensional nonlinear partial differential equations. Differential Equations and Dynamical Systems. 2015; 23(3): 317-325.
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  • [12] Misirli E and Gurefe Y. The Exp-function method to solve the generalized Burgers-Fisher equation. Nonlinear Science Letter A. 2010; 1: 323-328.
  • [13] Misirli E and Gurefe Y. Exact solutions of the Drinfel’d–Sokolov–Wilson equation using the exp-function method. Applied Mathematics and Computation. 2010; 216(9): 2623-2627.
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  • [15] Gurefe Y and Misirli E. Exp-function method for solving nonlinear evolution equations with higher order nonlinearity. Computers & Mathematics with Applications. 2011; 61(8): 2025-2030.
  • [16] Özpinar F, Baskonus, HM and Bulut H. On the complex and hyperbolic structures for the (2+ 1)-dimensional boussinesq water equation. Entropy. 2015; 17(12): 8267-8277.
  • [17] Yan ZY. New families of nontravelling wave solutions to a new (3 + 1)-dimensional potential-YTSF equation. Physics Letters A. 2003; 318: 78–83.
  • [18] Ma WX, Huang T and Zhang Y. A multiple exp-function method for nonlinear differential equations and its application. Physica Scripta. 2010; 82(6): 065003.
  • [19] Zhang S and Zhang HQ. A transformed rational function method for (3+ 1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation. Pramana. 2011; 76(4): 561-571.
  • [20] Roshid HO. Lump solutions to a (3+ 1)-dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) like equation. International Journal of Applied and Computational Mathematics. 2017; 3: 1455-1461.
  • [21] Tan, W. and Dai, Z. Dynamics of kinky wave for ($$$$)-dimensional potential Yu–Toda–Sasa–Fukuyama equation. Nonlinear Dynamics. 2016; 85(2): 817-823.
  • [22] Zayed EME and Ibrahim SH, 2013. The two variable (G'/G, 1/G)-expansion method for finding exact traveling wave solutions of the (3+ 1)-dimensional nonlinear potential Yu-Toda-Sasa-Fukuyama equation. In 2013 International Conference on Advanced Computer Science and Electronics Information (ICACSEI 2013). Atlantis Press.
  • [23] Zeng XP, Dai ZD, Li DL. New periodic soliton solutions for (3 + 1)-dimensional potential-YTSF equation. Chaos, Solitons Fractals. 2009; 42: 657–661.
  • [24] Zhao Z and He L. Multiple lump solutions of the (3+ 1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation. Applied Mathematics Letters. 2019; 95: 114-121.
  • [25] Dong MJ, Tian, SF, Wang XB and Zhang TT. Lump-type solutions and interaction solutions in the (3+ 1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation. Analysis and Mathematical Physics. 2019; 9(3): 1511-1523.
  • [26] Zheng X, Chen Y, Zhang H. Generalized extended tanh-function method and its application to (1+ 1)-dimensional dispersive long wave equation. Physics Letters A. 2003; 311(2-3):145-157.
  • [27] He JH and Wu XH. Exp-function method for nonlinear wave equations. Chaos, Solitons & Fractals. 2006; 30(3): 700-708.

Investigation of Nonlinear Wave Solutions in Fluid Mechanics

Year 2021, , 168 - 173, 31.12.2021
https://doi.org/10.46810/tdfd.932252

Abstract

In this study, the traveling wave solutions of the (3 + 1) -dimensional potential Yu-Toda-Sasa-Fukuyama (YTSF) equation were get using the modified exponential function method (MEFM). When the solution functions found are examined, it is seen that there are trigonometric, hyperbolic and rational functions. The solution functions obtained were checked by Wolfram Mathematica software, which provided the (3 + 1) -dimensional potential Yu-Toda-Sasa-Fukuyama (YTSF) equation. Two and three dimensional and contour graphs of the solution function were found by determining the appropriate parameters.

References

  • [1] Yang XF, Deng ZC, Wei YA. Riccati-Bernoulli sub-ODE method for nonlinear partial differential equations and its application. Advances in Difference equations. 2015; (1): 1-17.
  • [2] Baskonus HM, Bulut H. Exponential prototype structures for (2+1)-dimensional Boiti-Leon-Pempinelli systems in mathematical physics. Waves in Random and Complex Media. 2016; 26(2):189-196.
  • [3] Liu CS. Trial equation method and its applications to nonlinear evolution equations. Acta Physica Sinica. 2005; 54(6): 2505-2509.
  • [4] Liu CS. Trial equation method to nonlinear evolution equations with rank inhomogeneous: mathematical discussions and its applications. CoTPh. 2006; 45(2): 219-223.
  • [5] Abdelrahman MA. A note on Riccati-Bernoulli Sub-ODE method combined with complex transform method applied to fractional differential equations. Nonlinear Engineering. 2018; 7(4): 279-285.
  • [6] Bulut H, Baskonus HM and Pandir Y. The modified trial equation method for fractional wave equation and time fractional generalized Burgers equation. In Abstract and Applied Analysis Hindawi. 2013; Vol. 2013.
  • [7] Gurefe Y, Misirli E, Sonmezoglu A and Ekici M. Extended trial equation method to generalized nonlinear partial differential equations. Applied Mathematics and Computation. 2013; 219(10): 5253-5260.
  • [8] Elwakil SA, El-Labany SK, Zahran MA and Sabry R. Modified extended tanh-function method for solving nonlinear partial differential equations. Physics Letters A. 2002; 299(2-3): 179-188.
  • [9] Fan E and Hon YC. Applications of extended tanh method to ‘special’types of nonlinear equations. Applied Mathematics and Computation. 2003; 141(2-3): 351-358.
  • [10] Hosseini K and Gholamin P. Feng’s first integral method for analytic treatment of two higher dimensional nonlinear partial differential equations. Differential Equations and Dynamical Systems. 2015; 23(3): 317-325.
  • [11] Zheng X, Chen Y and Zhang H. Generalized extended tanh-function method and its application to (1+ 1)-dimensional dispersive long wave equation. Physics Letters A, 2003; 311(2-3): 145-157.
  • [12] Misirli E and Gurefe Y. The Exp-function method to solve the generalized Burgers-Fisher equation. Nonlinear Science Letter A. 2010; 1: 323-328.
  • [13] Misirli E and Gurefe Y. Exact solutions of the Drinfel’d–Sokolov–Wilson equation using the exp-function method. Applied Mathematics and Computation. 2010; 216(9): 2623-2627.
  • [14] Baskonus HM and Bulut H. Regarding on the prototype solutions for the nonlinear fractional-order biological population model. In AIP Conference Proceedings AIP Publishing LLC. 2016; 1738: 1.
  • [15] Gurefe Y and Misirli E. Exp-function method for solving nonlinear evolution equations with higher order nonlinearity. Computers & Mathematics with Applications. 2011; 61(8): 2025-2030.
  • [16] Özpinar F, Baskonus, HM and Bulut H. On the complex and hyperbolic structures for the (2+ 1)-dimensional boussinesq water equation. Entropy. 2015; 17(12): 8267-8277.
  • [17] Yan ZY. New families of nontravelling wave solutions to a new (3 + 1)-dimensional potential-YTSF equation. Physics Letters A. 2003; 318: 78–83.
  • [18] Ma WX, Huang T and Zhang Y. A multiple exp-function method for nonlinear differential equations and its application. Physica Scripta. 2010; 82(6): 065003.
  • [19] Zhang S and Zhang HQ. A transformed rational function method for (3+ 1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation. Pramana. 2011; 76(4): 561-571.
  • [20] Roshid HO. Lump solutions to a (3+ 1)-dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) like equation. International Journal of Applied and Computational Mathematics. 2017; 3: 1455-1461.
  • [21] Tan, W. and Dai, Z. Dynamics of kinky wave for ($$$$)-dimensional potential Yu–Toda–Sasa–Fukuyama equation. Nonlinear Dynamics. 2016; 85(2): 817-823.
  • [22] Zayed EME and Ibrahim SH, 2013. The two variable (G'/G, 1/G)-expansion method for finding exact traveling wave solutions of the (3+ 1)-dimensional nonlinear potential Yu-Toda-Sasa-Fukuyama equation. In 2013 International Conference on Advanced Computer Science and Electronics Information (ICACSEI 2013). Atlantis Press.
  • [23] Zeng XP, Dai ZD, Li DL. New periodic soliton solutions for (3 + 1)-dimensional potential-YTSF equation. Chaos, Solitons Fractals. 2009; 42: 657–661.
  • [24] Zhao Z and He L. Multiple lump solutions of the (3+ 1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation. Applied Mathematics Letters. 2019; 95: 114-121.
  • [25] Dong MJ, Tian, SF, Wang XB and Zhang TT. Lump-type solutions and interaction solutions in the (3+ 1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation. Analysis and Mathematical Physics. 2019; 9(3): 1511-1523.
  • [26] Zheng X, Chen Y, Zhang H. Generalized extended tanh-function method and its application to (1+ 1)-dimensional dispersive long wave equation. Physics Letters A. 2003; 311(2-3):145-157.
  • [27] He JH and Wu XH. Exp-function method for nonlinear wave equations. Chaos, Solitons & Fractals. 2006; 30(3): 700-708.
There are 27 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

Tolga Aktürk 0000-0002-8873-0424

Yusuf Gürefe 0000-0002-7210-5683

Publication Date December 31, 2021
Published in Issue Year 2021

Cite

APA Aktürk, T., & Gürefe, Y. (2021). Akışkanlar Mekaniğinde Doğrusal Olmayan Dalga Çözümlerinin İncelenmesi. Türk Doğa Ve Fen Dergisi, 10(2), 168-173. https://doi.org/10.46810/tdfd.932252
AMA Aktürk T, Gürefe Y. Akışkanlar Mekaniğinde Doğrusal Olmayan Dalga Çözümlerinin İncelenmesi. TDFD. December 2021;10(2):168-173. doi:10.46810/tdfd.932252
Chicago Aktürk, Tolga, and Yusuf Gürefe. “Akışkanlar Mekaniğinde Doğrusal Olmayan Dalga Çözümlerinin İncelenmesi”. Türk Doğa Ve Fen Dergisi 10, no. 2 (December 2021): 168-73. https://doi.org/10.46810/tdfd.932252.
EndNote Aktürk T, Gürefe Y (December 1, 2021) Akışkanlar Mekaniğinde Doğrusal Olmayan Dalga Çözümlerinin İncelenmesi. Türk Doğa ve Fen Dergisi 10 2 168–173.
IEEE T. Aktürk and Y. Gürefe, “Akışkanlar Mekaniğinde Doğrusal Olmayan Dalga Çözümlerinin İncelenmesi”, TDFD, vol. 10, no. 2, pp. 168–173, 2021, doi: 10.46810/tdfd.932252.
ISNAD Aktürk, Tolga - Gürefe, Yusuf. “Akışkanlar Mekaniğinde Doğrusal Olmayan Dalga Çözümlerinin İncelenmesi”. Türk Doğa ve Fen Dergisi 10/2 (December 2021), 168-173. https://doi.org/10.46810/tdfd.932252.
JAMA Aktürk T, Gürefe Y. Akışkanlar Mekaniğinde Doğrusal Olmayan Dalga Çözümlerinin İncelenmesi. TDFD. 2021;10:168–173.
MLA Aktürk, Tolga and Yusuf Gürefe. “Akışkanlar Mekaniğinde Doğrusal Olmayan Dalga Çözümlerinin İncelenmesi”. Türk Doğa Ve Fen Dergisi, vol. 10, no. 2, 2021, pp. 168-73, doi:10.46810/tdfd.932252.
Vancouver Aktürk T, Gürefe Y. Akışkanlar Mekaniğinde Doğrusal Olmayan Dalga Çözümlerinin İncelenmesi. TDFD. 2021;10(2):168-73.