APPLICATION OF THE EXTENDED TRIAL EQUATION METHOD TO THE NONLINEAR EVOLUTION EQUATIONS

APPLICATION OF THE EXTENDED TRIAL EQUATION METHOD TO THE NONLINEAR EVOLUTION EQUATIONS

In this paper we investigate the exact solutions of the nonlinearpartial differential equations. We have applied the extended trial equationmethod to nonlinear partial differential equations. By using this method wehave successfully obtained analytical solutions of the two-dimensional Bratutype equation. We think that this method can also be applied to other nonlinear evolution equations

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  • Malfliet, W. and Hereman, W., The tanh method. I. Exact solutions of nonlinear evolution and wave equations. Physica Scripta. 54 (1996), no. 6, 563-568.
  • Fan, E. G., Extended tanh-function method and its applications to nonlinear equations. Phys. Lett. A 277 (2000), no. 4-5, 212-218.
  • Abdou, M. A., The extended tanh method and its applications for solving nonlinear physical models. Appl. Math. Comput. 190 (2007), no. 1, 988-996.
  • Wazwaz, A. M., The extended tanh method for abundant solitary wave solutions of nonlinear wave equations. Appl. Math. Comput. 187 (2007), no. 2, 1131-1142.
  • Bin, Z., (G’/G)-Expansion method for solving fractional partial differential equations in the theory of mathematical physics. Commun. Theor. Phys. 58 (2012), no. 5, 623-630.
  • Wang, M., Li, X and Zhang, J., The (G’/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. Phys. Lett. A 372 (2008), no. 4, 417-423.
  • Zhang, S., Dong, L., Ba, J. M. and Sun, Y. N., The (G’/G)-expansion method for a discrete nonlinear Schrdinger equation. Pramana - J. Phys. 74 (2010), no. 2, 207-218.
  • Abazari, R., The (G’/G)-expansion method for Tzitzica type nonlinear evolution equations. Math. Comput. Model. 52 (2010), no. 9-10, 1834-1845.
  • Fan, E. and Zhang H., A note on the homogeneous balance method. Phys. Lett. A 246 (1998), no. 5, 403-406.
  • Wang, M., Solitary wave solutions for variant Boussinesq equations. Phys. Lett. A 199 (1995), no. 3-4, 169-172.
  • Jumarie, G., Cauchys integral formula via the modified RiemannLiouville derivative for an- alytic functions of fractional order. Appl. Math. Lett. 23 (2010), no. 12, 1444-1450.
  • Wang, M. L., Exact solutions for a compound KdV-Burgers equation. Phys. Lett. A 213 (1996), 279-287.
  • Wazwaz, A. M., A sine-cosine method for handlingnonlinear wave equations. Math. Comput. Model. 40 (2004), no. 5-6, 499-508.
  • Hirota, R. J., Exact N-soliton solutions of a nonlinear wave equation. J. Math. Phys. 14 (1973), no. 7, 805-809. [15] Hirota, R. and Satsuma, J. , Soliton solutions of a coupled Korteweg-de Vries equation. Phys. Lett. A 85 (1981), no. 8-9, 407-408.
  • Liu, C. S., Trial equation method and its applications to nonlinear evolution equations. Acta Physica Sinica 54 (2005), no. 6, 501-514.
  • Liu, C. S., Trial equation method to nonlinear evolution equations with eank inhomogeneous: mathematical discussions and its applications. Commun. Theor. Phys. 45 (2006), no. 2, 219- 223.
  • Liu, C. S., A New trial equation method and its applications. Commun. Theor. Phys. 45 (2006), no. 3, 395-397. [19] Pandir, Y., Gurefe, Y., Kadak, U. and Misirli, E., Classification of exact solutions for some nonlinear partial differential equations with generalized evolution. Abstr. Appl. Anal. (2012), Article ID 478531, 16 pages, doi:10.1155/2012/478531.
  • Boyd, J.P., An analytical and numerical study of the two-dimensional Bratu equation. Journal of Scientific Computing 1 (1986), no. 2, 183-206.
  • Misirli, E. and Gurefe Y., Exp-Function method for solving nonlinear evolution equations. Math. Comput. Appl. 16 (2011), no. 1, 258-266.
  • Department of Mathematics, Ege University, Izmir-TURKEY
  • E-mail address: meryem.odabasi@ege.edu.tr, emine.misirli@ege.edu.tr