Comparison Of (G′/G)-Methods for Finding Exact Solutions of the Drinfeld-Sokolov System
-
Durmus Daghan
,
Ozlem Yildiz
Abstract
Nonlinear Drinfeld-Sokolov system is studied analytically by using four different methods ((G′/G)-expansion, direct algebraic, different form of the (G′/G)-expansion methods, and direct integration) and the results are found numerically. New exact and numeric solutions are given and the comparison of the results obtained from these different methods, methods themselves and numerical results are discussed in detail. It is found that the (G′/G)-expansion and different form of the (G′/G)-expansion methods are really coincide and effective methods in the view of finding different solutions that cannot be obtained by using the direct integration for Drinfel-Sokolov system.
References
[1] KUDRYASHOV, N. A.: Seven common errors in finding exact solutions of nonlinear differential equations, Commun. Nonlinear Sci. Numer. Simul. 14 (2009), 3507-3529.10.1016/j.cnsns.2009.01.023Search in Google Scholar
[2] WANG, M. L.-LI, X.-ZHANG, J.: The (G′/G)-expansion method and traveling wave solutions of nonlinear evolution equations in mathematical physics, Phys. Lett. A 372 (2008), 417-423.10.1016/j.physleta.2007.07.051Search in Google Scholar
[3] LI, L-X.-WANG,M. L.: The (G′/G)-expansion method and travelling wave solutions for a higher-order nonlinear Schrdinger equation, Appl. Math. Comput. 208 (2009), 440-445.10.1016/j.amc.2008.12.005Search in Google Scholar
[4] ZHANG, H.: A direct algebraic method applied to obtain complex solutions of some nonlinear partial differential equations, Chaos Solitons Fractals 39 (2009), 1020-1026.10.1016/j.chaos.2007.03.002Search in Google Scholar
[5] WANG, JP.: A list of 1+1 dimensional integrable equations and their properties, J. Nonlinear Math. Phys. 9 (2002), 213-233.10.2991/jnmp.2002.9.s1.18Search in Google Scholar
[6] OLVER, PJ.: Applications of Lie Groups to Differential Equations, Springer, New York, 1993.10.1007/978-1-4612-4350-2Search in Google Scholar
[7] GOKTAS, U.-HEREMAN, E.: Symbolic computation of conserved densities for systems of nonlinear evolution equations, J. Symbolic Comput. 24 (1997), 591-621.10.1006/jsco.1997.0154Search in Google Scholar
[8] GURSES, M.-KARASU, A.: Integrable KdV systems: Recursion operators of degree four, Phys. Lett. A 251 (1999), 247-249.10.1016/S0375-9601(98)00910-4Search in Google Scholar
[9] SWEET, E.-VAN GORDER, R. A.: Analytical solutions to a generalized Drinfel’d- Sokolov equation related to DSSH and KdV6, Appl. Math. Comput. 216 (2010), 2783-2791.10.1016/j.amc.2010.03.128Search in Google Scholar
[10] SWEET, E.-VAN GORDER, R. A.: Trigonometric and hyperbolic type solutions to a generalized Drinfel’d-Sokolov equation, Appl. Math. Comput. 217 (2010), 4147-4166.10.1016/j.amc.2010.09.064Search in Google Scholar
[11] SWEET, E.-VAN GORDER, R. A.: Exponential-type solutions to a generalized Drinfel’d-Sokolov equation, Physica Scripta 8 (2010), 035006.10.1088/0031-8949/82/03/035006Search in Google Scholar
[12] UGURLU, Y.-KAYA, D.: Exact and numerical solutions of generalized Drinfeld-Sokolov equations, Phys. Lett. A 372 (2008), 2867-2873.10.1016/j.physleta.2008.01.003Search in Google Scholar
[13] HU, J.: A new method of exact travelling wave solution for coupled nonlinear differential equations, Phys. Lett. A 322 (2004), 211-216.10.1016/j.physleta.2004.01.074Search in Google Scholar
[14] SWEET, E.-VAN GORDER, R. A.: Traveling wave solutions (u, v) to a generalized Drinfel’d-Sokolov system which satisfy u = a1vm+a0, Appl. Math. Comput. 218 (2012), 9911-9921.10.1016/j.amc.2012.03.078Search in Google Scholar
[15] BEKIR, A.: Applications of the extended tanh method for coupled nonlinear evolution equations, Commun. Nonlinear Sci. Numer. Simul. 13 (2008), 1748-1757. 10.1016/j.cnsns.2007.05.001Search in Google Scholar
[16] WAZWAZ, A. M.: Exact and explicit travelling wave solutions for the nonlinear Drinfeld- Sokolov system, Commun. Nonlinear Sci. Numer. Simul. 11 (2006), 311-325.10.1016/j.cnsns.2004.10.001Search in Google Scholar
[17] EL-WAKIL, S. A.-ABDOU, M. A.: Modified extended tanh-function method for solving nonlinear partial differential equations, Chaos Solitons Fractals 31 (2007), 1256-1264. 10.1016/j.chaos.2005.10.072Search in Google Scholar
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Articles in the same Issue
- Fuzzy Pseudo Subalgebras and Ideals of Pseudo D-Algebras
- Five Curious Congruences Modulo p2
- On the Hybrid Mean Value Involving Dedekind Sums and Kloosterman Sums
- Constructing New Crossed Group Categories Over Weak Hopf Group Algebras
- Generalization of Hilbert Inequality with Some Parameters
- Some Applications of Differential Subordination of p-Valent Functions
- Coefficient Estimates and Quasi-Subordination Properties Associated with Certain Subclasses of Analytic and Bi-Univalent Functions
- On Properties of Entire Solutions of Difference Equations and Difference Polynomials
- On the Ψ-Strong Stability of Nonlinear Lyapunov Matrix Differential Equations
- On the Existence of Solutions of Ordinary Differential Equations in Banach Spaces
- Global Dynamics of a Delayed n + m-Species Competition Predator-Prey System on Time Scales
- Comparison Of (G′/G)-Methods for Finding Exact Solutions of the Drinfeld-Sokolov System
- A Generalization of Cyclic Amenability of Banach Algebras
- n-Weak Module Amenability of Triangular Banach Algebras
- On a Class of Operator-Differential Equations of the Third Order With Multiple Characteristics on the Whole Axis in the Weighted Space
- Optimality Conditions for Vector Equilibrium Problems with Set-Valued Mappings and Cone Constraints
- Classification of the Blaschke Isoparametric Hypersurfaces in Lorentzian Space Forms
- A New Proof of a Theorem on Long Cycles
