×

Topological and non-topological solitons of the generalized Klein-Gordon equations. (English) Zbl 1176.35150

Summary: This paper obtains the 1-soliton solution of five various forms of the generalized nonlinear Klein-Gordon equations. The solitary wave ansatz is used to obtain the soliton solutions of each of these cases. Both topological as well as non-topological soliton solutions are obtained depending on the type of nonlinearity in question. The conserved quantities are also calculated for each of these five forms of generalized nonlinear Klein-Gordon equations. Each of these forms can be reduced to the previously known results, as special cases.

MSC:

35Q51 Soliton equations
35C08 Soliton solutions
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] 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, Communications in Nonlinear Science and Numerical Simulation, 14, 3, 718-723 (2009) · Zbl 1221.65272
[2] Biswas, A.; Zony, C.; Zerrad, E., Soliton perturbation theory for the quadratic nonlinear Klein-Gordon equations, Applied Mathematics and Computation, 203, 1, 153-156 (2008) · Zbl 1161.35480
[3] Chen, G., Solution of the Klein-Gordon for exponential scalar and vector potentials, Physics Letters A, 339, 3-5, 300-303 (2005) · Zbl 1145.81353
[4] Deng, X.; Zhao, M.; Li, X., Travelling wave solutions for a nonlinear variant of the phi-four equation, Mathematical and Computer Modelling, 49, 3-4, 617-622 (2009) · Zbl 1165.35415
[5] Ebaid, A., Exact solutions for the generalized Klein-Gordon equation via a transformation and Exp-function method and comparison with Adomian’s method, Journal of Computational and Applied Mathematics, 223, 1, 278-290 (2009) · Zbl 1155.65079
[6] Elgarayahi, A., New periodic wave solutions for the shallow water equations and the generalized Klein-Gordon equation, Communications in Nonlinear Science and Numerical Simulation, 13, 5, 877-888 (2008) · Zbl 1221.35332
[7] Feng, D.; Li, J., Exact explicit travelling wave solutions for the \((n + 1)\)-dimensional \(\Phi^6\) field model, Physics Letters A, 369, 255-261 (2007) · Zbl 1209.81148
[8] Kudryashov, N. A., Seven common errors in finding exact solutions of nonlinear differential equations, Communications in Nonlinear Science and Numerical Simulation, 14, 9-10 (2009)
[9] Mustafa Inc., New compacton and solitary pattern solutions of the nonlinear modified dispersive Klein-Gordon equations, Chaos, Solitons & Fractals, 33, 4, 1275-1284 (2007) · Zbl 1137.35421
[10] Sassaman, R.; Biswas, A., Soliton perturbation theory for phi-four model and nonlinear Klein-Gordon equations, Communications in Nonlinear Science and Numerical Simulations, 14, 8, 3226-3229 (2009) · Zbl 1221.35305
[11] Sirendaoreji, Exact travelling wave solutions for four forms of nonlinear Klein-Gordon equations, Physics Letters A, 363, 440-447 (2007) · Zbl 1197.35166
[12] Wazwaz, A. M., Solutions of compact and noncompact structures for nonlinear Klein-Gordon type equation, Applied Mathematics and Computation, 134, 2-3, 487-500 (2003) · Zbl 1027.35119
[13] Wazwaz, A. M., The tanh and sine-cosine methods for compact and noncompact solutions of the nonlinear Klein-Gordon equation, Applied Mathematics and Computation, 167, 2, 1179-1195 (2005) · Zbl 1082.65584
[14] Wazwaz, A. M., Generalized forms of the phi-four equation with compactons, solitons and periodic solutions, Mathematics and Computers in Simulations, 69, 5-6, 580-588 (2005) · Zbl 1078.35526
[15] Wazwaz, A. M., New travelling wave solutions to the Boussinesq and the Klein-Gordon equations, Communications in Nonlinear Science and Numerical Simulation, 13, 5, 889-901 (2008) · Zbl 1221.35372
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.