On The Prototype Solutions of Symmetric Regularized Long Wave Equation by Generalized Kudryashov Method
Volume 1, Issue 2, August 2015, Pages: 10-16
Received: Aug. 19, 2015;
Accepted: Nov. 7, 2015;
Published: Dec. 14, 2015
Views 3501 Downloads 144
Hasan Bulut, Department of Mathematics, Firat University, Elazig, Turkey
Haci Mehmet Baskonus, Department of Computer Engineering, Tunceli University, Tunceli, Turkey
Eren Cüvelek, Department of Mathematics, Firat University, Elazig, Turkey
In this study, we have applied the generalized kudryashov method to the symmetric regularized long wave equation for obtaining some new analytical solutions such as trigonometric function solution, exponential function solution, complexl function solution, hyperbolic function solution after giving the fundamental properties of method. Afterwards, we have observed that these analytical solutions are verified the symmetric regularized long wave equation by means of Wolfram Mathematica 9. Then, we have drawn two and three dimensional surfaces of analytical solutions. Finally, we have submitted a conclusion to literature.
Haci Mehmet Baskonus,
On The Prototype Solutions of Symmetric Regularized Long Wave Equation by Generalized Kudryashov Method, Mathematics Letters.
Vol. 1, No. 2,
2015, pp. 10-16.
G. K. Watugala, Sumudu Transform: A New Integral Transform to Solve Differantial Equations and Control Engineering Problems, International Journal of Mathematical Education in Science and Technology, 1993, 24, 35-43.
Y. Pandir, New exact solutions of the generalized Zakharov–Kuznetsov modified equal-width equation, Pramana journal of physics, 2014, 82(6), 949–964.
H. Bulut, H. M. Baskonus and F. B. M. Belgacem, The Analytical Solutions of Some Fractional Ordinary Differential Equations by Sumudu Transform Method, Abstract and Applied Analysis, 2013.
A. M. Wazwaz, The tanh method: solitons and periodic solutions for Dodd-Bullough-Mikhailov and Tzitzeica- Dodd-Bullough equations, Chaos, Solitons and Fractals, 2005, 25, 55-56.
C.S. Liu, A new trial equation method and its applications, Communications in Theoretical Physics,2006, 45(3), 395-397.
C.S. Liu, Trial Equation Method to Nonlinear Evolution Equations with Rank Inhomogeneous: Mathematical Discussions and Its Applications, Communications in Theoretical Physics, 2006, 45(2), 219–223.
H. Bulut, Y. Pandir, H. M. Baskonus, Symmetrical Hyperbolic Fibonacci Function Solutions of Generalized Fisher Equation with Fractional Order, AIP Conf. Proc.,2013, 1558, 1914 (2013).
Y. Pandir, Y. Gurefe, U, Kadak, and E. Misirli, Classifications of exact solutions for some nonlinear partial differential equations with generalized evolution, Abstract and Applied Analysis, vol.2012, Article ID 478531, 16 pages, 2012.
Ryabov, P. N., Sinelshchikov, D. I., and Kochanov, M. B., Application of the Kudryashov method for finding exact solutions of the high order nonlinear evolution equations, Applied Mathematics and Computation, 218(7), 3965–3972, (2011).
Kudryashov, N. A., One method for finding exact solutions of nonlinear differential equations, Communications in Nonlinear Science and Numerical Simulation, 17(6), 2248–2253, (2012).
Lee J., and Sakthivel, R., Exact travelling wave solutions for some important nonlinear physical models, Pramana—Journal of Physics, 80(5), 757–769, (2013).
Demiray, S.T., Pandir, Y., and Bulut, H., Generalized Kudryashov Method for Time-Fractional Differential Equations, Abstract and Applied Analysis, 2014, 13 pages, (2014).
J. Manafian and I. Zamanpour, Exact travelling wave solutions of the symmetric regularized long wave (SRLW) using analytical methods, Statistics, Optimization And Information Computing, 2, 47–55, 2014.