Frontiers of Mathematics in China >
Singular soliton solution and bifurcation analysis of Klein-Gordon equation with power law nonlinearity
Received date: 20 Jul 2012
Accepted date: 17 Oct 2012
Published date: 01 Feb 2013
Copyright
In this paper, the Klein-Gordon equation (KGE) with power law nonlinearity will be considered. The bifurcation analysis as well as the ansatz method of integration will be applied to extract soliton and other wave solutions. In particular, the second approach to integration will lead to a singular soliton solution. However, the bifurcation analysis will reveal several other solutions that are of prime importance in relativistic quantum mechanics where this equation appears.
Ming SONG , Zhengrong LIU , Essaid ZERRAD , Anjan BISWAS . Singular soliton solution and bifurcation analysis of Klein-Gordon equation with power law nonlinearity[J]. Frontiers of Mathematics in China, 2013 , 8(1) : 191 -201 . DOI: 10.1007/s11464-012-0252-z
| 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. Commun Nonlinear Sci Numer Simul, 2009, 14(3): 718-723
|
| 2 |
Biswas A, Ebadi G, Fessak M, Johnpillai A G, Johnson S, Krishnan E V, Yildirim A. Solutions of the perturbed Klein-Gordon equation in relativistic quantum mechanics. Iran J Sci Technol Trans A Sci (to appear)
|
| 3 |
Biswas A, Yildirim A, Hayat T, Aldossary O M, Sassaman R. Soliton perturbation theory for the generalized Klein-Gordon equation with full nonlinearity. Proc Rom Acad Ser A, 2012, 13(1): 32-41
|
| 4 |
Johnpillai A G, Yildirim A, Biswas A. Chiral solitons with Bohm potential by Lie group analysis and traveling wave hypothesis. Romanian J Phys, 2012, 57(3-4): 545-554
|
| 5 |
Sassaman R, Biswas A. Soliton perturbation theory for phi-four model and nonlinear Klein-Gordon equations. Commun Nonlinear Sci Numer Simul, 2009, 14(8): 3239-3249
|
| 6 |
Sassaman R, Biswas A. Topological and non-topological solitons of the generalized Klein-Gordon equation. Appl Math Comput, 2009, 215(1): 212-220
|
| 7 |
Sassaman R, Biswas A. Soliton solutions of the generalized Klein-Gordon equation by semi-inverse variational principle. Math Eng Sci Aerospace, 2011, 2(1): 99-104
|
| 8 |
Sassaman R, Biswas A. 1-soliton solution of the perturbed Klein-Gordon equation. Phys Express, 2011, 1(1): 9-14
|
| 9 |
Shakeri F, Dehghan M. Numerical solution of the Klein-Gordon equation via He’s variational iteration method. Nonlinear Dynam, 2007, 51(1-2): 89-97
|
| 10 |
Sirendaoreji. Exact travelling wave solutions for four forms of nonlinear Klein-Gordon equations. Phys Lett A, 2007, 363: 440-447
|
| 11 |
Song M, Cai J. Solitary wave solutions and kink wave solutions for a generalized Zakharov-Kuznetsov equation. Appl Math Comput, 2010, 217(4): 1455-1462
|
| 12 |
Song M, Hou X, Cao J. Solitary wave solutions and kink wave solutions of a generalized KdV-mKdV equation. Appl Math Comput, 2011, 217(12): 5942-5948
|
| 13 |
Song M, Shao S. Exact solitary wave solutions of the generalized (2+1)-dimensional Boussinesq equation. Appl Math Comput, 2010, 217(7): 3557-3563
|
| 14 |
Song M, Yang C. Exact traveling wave solutions of the Zakharov-Kuznetsov-Benjamin- Bona-Mahoney equation. Appl Math Comput, 2010, 216(11): 3234-3243
|
| 15 |
Song M, Yang C, Zhang B. Exact solitary wave solutions of the Kadomtsev-Petviashvili- Benjamin-Bona-Mahoney equation. Appl Math Comput, 2010, 217(4): 1334-1339
|
| 16 |
Triki H, Crutcher S, Yildirim A, Hayat T, Aldossary O M, Biswas A. Bright and dark solitons of the modified complex Ginzburg-Landau equation with parabolic and dualpower law nonlinearity. Romanian Rep Phys, 2012, 64(2): 367-380
|
| 17 |
Triki H, Yildirim A, Hayat T, Aldossary OM, Biswas A. Topological and non-topological soliton solutions of the Bretherton equation. Proc Romanian Acad Ser A, 2012, 13(2): 103-108
|
| 18 |
Wazwaz A M. The tanh and sine-cosine methods for compact and noncompact solutions of the nonlinear Klein-Gordon equation. Appl Math Comput, 2005, 167(2): 1179-1195
|
| 19 |
Wazwaz A M. Generalized forms of the phi-four equation with compactons, solitons and periodic solutions. Math Comput Simulation. 2005, 69(5-6): 580-588
|
| 20 |
Wen Z, Liu Z, Song M. New exact solutions for the classical Drinfel’d-Sokolov-Wilson equation. Appl Math Comput, 2009, 215(6): 2349-2358
|
/
| 〈 |
|
〉 |