New function method to the (n+1)-dimensional nonlinear problems

Tolga Aktürk, Yusuf Gürefe, Hasan Bulut


In this study, a new approach that assumes  and  is applied to construct the traveling wave solutions of the (N + 1)-dimensional double sine-Gordon and (N + 1)-dimensional double sinh-cosh-Gordon equations. Some new elliptic integral function solutions are respectively obtained by this method, and then these solutions are converted into the Jacobi elliptic function solutions. According these results, one can easily see that this method is very effective mathematical tool for the (N+1)-dimensional nonlinear physical problems.

Full Text:



Liu, C. S., (2005). Trial equation method and its applications to nonlinear evolution equations, Acta. Phys. Sin. 54, 2505-2509

Pandir, Y., Gurefe, Y., Kadak, U., & Misirli, E., (2012). Classification of exact solutions for some nonlinear partial differential equations with generalized evolution, Abstr. Appl. Anal. 2012, 16 pages

Pandir, Y., Gurefe, Y., & Misirli, E., (2013). Classification of exact solutions to the generalized Kadomtsev- Petviashvili equation, Phys. Scr. 87, 12 pages

Porubov, A.V., & Velarde, M.G., (1999). Exact periodic solutions of the complex Ginzburg-Landau equation, J. Math. Phys. 40(2), 884-896

Fan, E., (2000). Extended tanh-function method and its applications to nonlinear equations, Phys. Lett. A 277(4), 212-218

Kudryashov, N. A., (2012). One method for finding exact solutions of nonlinear differential equations, Commun. Nonl. Sci. Numer. Simul. 17, 2248-2253

Li, J.B., (2007). Exact traveling wave solutions and dynamical behavior for the (n + 1)-dimensional multiple sine-Gordon equation, Sci. in China Ser. A: Math. 50(2), 153-164

Lee, J., & Sakhtivel, R., (2010). Travelling wave solutions for (N+1)-dimensional nonlinear evolution equations, Pramana-J. Phys. 75(4), 565-578

Wang, D.S., Yan Z., & Li H., (2008). Some special types of solutions of a class of the (N+1)-dimensional nonlinear wave equation, Comput. Math. Appl. 56(6), 1569-1579

Shen, G., Sun, Y., & Xiong, Y., (2013). New travelling-wave solutions for Dodd-Bullough equation, J. Appl. Math. 2013, Article ID.364718, 5 pages

Sun, Y., (2014). New travelling wave solutions for Sine-Gordon equation, J. Appl. Math. 2014, Article ID.841416, 4 pages

Bulut, H., Akturk, T., & Gurefe, Y., (2014). Traveling wave solutions of the (N+1)-dimensional sin-cosine-Gordon equation, AIP Conference Proceedings, 1637(1), 145-149

Bulut, H., Akturk, T., & Gurefe, Y., (2015). An application of the new function method to the generalized double sinh-Gordon equation, AIP Conference Proceedings, 1648(370014), 4 pages

Akturk, T., (2015). Determining the exact solutions of some nonlinear partial differential equations by trial equation methods, Firat University, PhD Thesis



  • There are currently no refbacks.

Copyright (c) 2017 Tolga Aktürk

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


   ithe_170     crossref_284         ind_131_43_x_117_117  Scopus  EBSCO_Host    ULAKBIM     ZBMATH more...