Exact Solutions of the Two Dimensional KdV-Burger Equation by Generalized Kudryashov Method

Year 2021, , 617 - 624, 01.03.2021

Yusuf Pandır , Sahragül Eren

https://doi.org/10.21597/jist.713556

Cited By: 3

Abstract

In this article, the generalized Kudryashov method which provides the exact solutions is examined. It is possible to obtain new exact solutions of the nonlinear differential equations with this method. By implementing this developed method to the two-dimensional KdV-Burger equation, new exact solutions of this equation are found. This new exact solutions are the solutions that are not in the literature. In addition, two and three-dimensional graphics of these new exact solutions have been drawn and their physical behavior has been demonstrated.

Keywords

Genelleştirilmiş Kudryashov Yöntemi, Kısmi Türevli Diferansiyel Denklemler, iki Boyutlu KdV-Burger Denklemi, Tam Çözümler

References

• Akbar MA, Ali NHM, Mohyud-Din ST, 2013. The modified alternative -expansion method to nonlinear evolution equation: application to the (1+1)-dimensional Drinfel’d-Sokolov-Wilson equation. SpringerPlus 327:2-16.
• Demiray ST, Pandir Y, Bulut H, 2015. New solitary wave solutions of Maccari system. Ocean Engineering 103:153-159.
• Demiray ST, Pandir Y, Bulut H, 2015. New soliton solutions for Sasa-Satsuma equation. Waves in Random Complex Media 25(3): 417-418.
• Fu Z, Liu S, Liu S, Zhao Q, 2001. New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations. Physics Letters A 290: 72-76.
• Guo S, Zhou Y, 2010. The extended -expansion method and its applications to the Whitham-Broer-Kaup-Like equations and coupled Hirota–Satsuma KdV equations. Applied Mathematics and Computation 215: 3214-3221.
• Gurefe Y, Sonmezoglu A, Misirli E, 2011. Application of trial equation method to the nonlinear partial differential equations arising in mathematical physics. Pramana Journal of Physics 77(6): 1023-1029.
• Gurefe Y, Sonmezoglu A, Misirli E, 2012. Application of an irrational trial equation method to high dimensional nonlinear evolution equations. Journal of Advanced Mathematical Studies 5(1): 41-47.
• Gurefe, Y, Misirli E, Sonmezoglu A, Ekici M, 2013. Extended trial equation method to generalized nonlinear partial differential equations. Applied Mathematics Computation 219(10): 5253-5260.
• He JH, Wu X H, 2006. Exp-function method for nonlinear wave equations. Chaos, Soliton & Fractals 30: 700-708.
• Jeffrey A, Kakutani T, 1972. Weak nonlinear dispersive waves: a discussion centered around the Korteweg-de Vries equation. Society for Industrial Applied Mathematics 14: 582-643.
• Kudryashov NA, 2012. One method for finding exact solutions of nonlinear differential equations. Communication of Nonlinear Science and Numerical Simulation 17: 2248-2253.
• Lee J, Sakthivel R, 2013. Exact travelling wave solutions for some important nonlinear physical models. Pramana Journal of Physics 80: 757-769.
• Liu CS, 2006. Trial equation method for nonlinear evolution equations with rank inhomogeneous: mathematical discussions and applications. Communication in Theoretical Physics 45(2): 219-223.
• Liu CS, 2010. Applications of complete discrimination system for polynomial for classifications of traveling wave solutions to nonlinear differential equations. Computer Physics Communications 181(2): 317-324.
• Malfliet W, Hereman W, 1996. The Tanh method: I exact solutions of nonlinear evolution and wave equations. Physica Scripta 54: 563-568.
• Malfliet W, 2004. The tanh method: a tool for solving certain classes of nonlinear evolution and wave equations. Journal of Computational and Applied Mathematic 164-165: 529-541.
• Pandir Y, Gurefe Y, Kadak U, Misirli E, 2012. Classifications of exact solutions for some nonlinear partial differential equations with generalized evolution. Abstract and Applied Analysis 2012: 1-16.
• Pandir Y, Gurefe Y, Misirli E, 2013. Classification of exact solutions to the generalized Kadomtsev-Petviashvili equation. Physica Scripta 87(2): 1-12.
• Pandir Y, Gurefe Y, Misirli E, 2013. A multiple extended trial equation method for the fractional Sharma-Tasso-Olver equation. AIP Conference Proceedings 1558: 1927.
• Pandir Y, 2014. Symmetric Fibonacci function solutions of some nonlinear partial differential equations. Applied Mathematics and Information Sciences 8: 2237-2241.
• Pandir Y, Sonmezoglu A, Duzgun HH, Turhan N, 2015. Exact solutions of nonlinear Schrödinger’s equation by using generalized Kudryashov method. AIP Conference Proceedings 1648: 370004.
• Pandir Y, Demiray ST, Bulut H, 2016. A new approach for some NLDEs with variable coefficients. Optik 127: 11183-11190.
• Pandir Y, Turhan N, 2017. A new version of the generalized F-expansion method and its applications. AIP Conference Proceedings 1798: 020122.
• Pandir Y, 2017. A new type of the generalized F-expansion method and its application to Sine-Gordon equation. Celal Bayar University Journal of Science 13(3): 647-650.
• Ravi LK, Ray SS, Sahoo S, 2017. New exact solutions of coupled Boussinesq-Burgers equations by exp-function method. Journal of Ocean Engineering and Science 2: 34-46.
• Ryabov PN, Sinelshchikov DI, Kochanov, MB, Application of the Kudryashov method for finding exact solutions of the high order nonlinear evolution equations. Applied Mathematics and Computation 218: 3965-3972.
• Seadawy AR, 2013. Travelling wave solution of two dimensional nonlinear KdV-Burgers equation. Applied Mathematical Sciences 7(68): 3367-3377.
• Shakeel M, Mohyud-Din ST, 2015. New -expansion method and its application to the Zakharov-Kuznetsov–Benjamin-Bona-Mahony (ZK–BBM) equation. Journal of the Association of Arab Universities for Basic & Applied Science 18(1): 66-81.
• Shen S, Pan Z, 2003. A note on the Jacobi elliptic function expansion method. Physics Letters A 308: 143-148.
• Tandogan YA, Pandir Y, Gurefe Y, 2013. Solutions of the nonlinear differential equations by use of modified Kudryashov method. Turkish Journal of Mathematics Computer Science 1: 54-60.
• Zhang J, Jiang F, Zhao X, 2010. An improved -expansion method for solving nonlinear evolution equations. International Journal of Computational Mathematics 87(8): 1716-1725.