Abstract
This paper obtains the topological and non-topological 1-soliton solution of the Klein–Gordon equation in 1+2 dimensions. There are five various forms of this equation that will be studied. The solitary wave ansatz will be used to carry out the integration.
Similar content being viewed by others
References
Basak, K.C., Ray, P.C., Bera, R.K.: Solution of non-linear Klein–Gordon equation with a quadratic non-linear term by Adomian decomposition method. Commun. Nonlinear Sci. Numer. Simul. 14(3), 718–723 (2009)
Biswas, A., Zony, C., Zerrad, E.: Soliton perturbation theory for the quadratic nonlinear Klein–Gordon equations. Appl. Math. Comput. 203(1), 153–156 (2008)
Chen, G.: Solution of the Klein–Gordon for exponential scalar and vector potentials. Phys. Lett. A 339(3–5), 300–303 (2005)
Comay, E.: Difficulties with the Klein–Gordon equation. Apeiron 11(3), 1–18 (2004)
Deng, X., Zhao, M., Li, X.: Travelling wave solutions for a nonlinear variant of the phi-four equation. Math. Comput. Model. 49(3–4), 617–622 (2009)
Ebaid, A.: Exact solutions for the generalized Klein–Gordon equation via a transformation and Exp-function method and comparison with Adomian’s method. J. Comput. Appl. Math. 223(1), 278–290 (2009)
Elgarayahi, A.: New periodic wave solutions for the shallow water equations and the generalized Klein–Gordon equation. Commun. Nonlinear Sci. Numer. Simul. 13(5), 877–888 (2008)
Fang, Y.-f.: A direct proof of global existence for the Dirac–Klein–Gordon equations in one space dimension. Taiwan. J. Math. 8(1), 33–41 (2004)
Feng, D., Li, J.: Exact explicit travelling wave solutions for the (n+1)-dimensional Φ 6 field model. Phys. Lett. A 369, 255–261 (2007)
Kudryashov, N.A.: Seven common errors in finding exact solutions of nonlinear differential equations. Commun. Nonlinear Sci. Numer. Simul. 14(9–10) (2009)
Mustafa Inc.: New compacton and solitary pattern solutions of the nonlinear modified dispersive Klein–Gordon equations. Chaos Solitons Fractals 33(4), 1275–1284 (2007)
Sassaman, R., Biswas, A.: Soliton perturbation theory for phi-four model and nonlinear Klein–Gordon equations. Commun. Nonlinear Sci. Numer. Simul. 14(8), 3226–3229 (2009)
Sassaman, R., Biswas, A.: Topological and non-topological solitons of the generalized Klein–Gordon equations. Appl. Math. Comput. 215(1), 212–220 (2009)
Shakeri, F., Dehghan, M.: Numerical solution of the Klein–Gordon equation via He’s variational iteration method. Nonlinear Dyn. 51(1–2), 89–97 (2007)
Sirendaoreji, Exact travelling wave solutions for four forms of nonlinear Klein–Gordon equations. Phys. Lett. A 363, 440–447 (2007)
Wazwaz, A.M.: Solutions of compact and noncompact structures for nonlinear Klein–Gordon type equation. Appl. Math. Comput. 134(2–3), 487–500 (2003)
Wazwaz, A.M.: The tanh and sine–cosine methods for compact and noncompact solutions of the nonlinear Klein–Gordon equation. Appl. Math. Comput. 167(2), 1179–1195 (2005)
Wazwaz, A.M.: Generalized forms of the phi-four equation with compactons, solitons and periodic solutions. Math. Comput. Simul. 69(5–6), 580–588 (2005)
Wazwaz, A.M.: New travelling wave solutions to the Boussinesq and the Klein–Gordon equations. Commun. Nonlinear Sci. Numer. Simul. 13(5), 889–901 (2008)
Zheng, Y., Lai, S.: A study on three types of nonlinear Klein–Gordon equations. Dyn. Contin. Discrete Impuls. Syst., Ser. B 16(2), 271–279 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sassaman, R., Biswas, A. Topological and non-topological solitons of the Klein–Gordon equations in 1+2 dimensions. Nonlinear Dyn 61, 23–28 (2010). https://doi.org/10.1007/s11071-009-9628-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-009-9628-3