Abstract
The aim of this paper is to present solitary wave solutions of two different forms of Klein–Gordon equations with full nonlinearity. The \(\left( \frac{G'}{G}\right) \)-expansion method is applied to solve the governing equations and then exact 1-soliton solutions are obtained. It is shown that this method provides us with a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abazari R (2013) Solitary-wave solutions of the Klein-Gordon equation with quintic nonlinearity. J Appl Mech Tech Phys 54:397–403
Biswas A, Yildirim A, Hayat T, Aldossary OM, Sassaman R (2012) Soliton perturbation theory of the generalized Klein-Gordon equation with full nonlinearity. Proc Romanian Acad Ser A 13:32–41
Ebadi G, Biswas A (2011) The \(\left(\frac{G^{\prime }}{G}\right)\) method and topological soliton solution of the \(K(m, n)\) equation. Commun Nonlinear Sci Numer Simul 16:2377–2382
Fabian AL, Kohl R, Biswas A (2009) Perturbation of topological solitons due to sine-Gordon equation and its type. Commun Nonlinear Sci Numer Simul 14:1227–1244
Infeld E, Rowlands G (2000) Nonlinear waves. Cambridge University Press, Solitons and Chaos, Cambridge
Sassaman R, Biswas A (2009) Topological and non-topological solitons of the generalized Klein-Gordon equations. Appl Math Comput 215:212–220
Sassaman R, Biswas A (2010) Topological and non-topological solitons of the Klein-Gordon equations in 1+2 dimensions. Nonlinear Dyn 61:23–28
Wang ML, Li XZ, Zhang JL (2008) The \(\left(\frac{G^{\prime }}{G}\right)\)- expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. Phys Lett A 372(4):417–423
Wazwaz AM (2006) Compactons, solitons and periodic solutions for some forms of nonlinear Klein-Gordon equations. Chaos Solitons Fractals 28:1005–1013
Zayed E, Gepreel KA (2009) Some applications of the \(\left(\frac{G^{\prime }}{G}\right)\)-expansion method to non-linear partial differential equations. Appl Math Comput 212(1):113
Zhang S, Tong JL, Wang W (2008) A generalized \(\left(\frac{G^{\prime }}{G}\right)\)-expansion method for the mKdV equation with variable coefficients. Phys Lett A 372(13):2254–2257
Zhang H (2009) New application of the \(\left(\frac{G^{\prime }}{G}\right)\)-expansion method. Commun Nonlinear Sci Numer Simul 14:3220–3225
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Pierangelo Marcati.
Rights and permissions
About this article
Cite this article
Mirzazadeh, M., Eslami, M. & Biswas, A. Soliton solutions of the generalized Klein–Gordon equation by using \(\left( \frac{G^{\prime }}{G}\right) \)-expansion method. Comp. Appl. Math. 33, 831–839 (2014). https://doi.org/10.1007/s40314-013-0098-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40314-013-0098-3