scholarly journals Topological Soliton Solution and Bifurcation Analysis of the Klein-Gordon-Zakharov Equation in(1+1)-Dimensions with Power Law Nonlinearity

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Ming Song ◽  
Bouthina S. Ahmed ◽  
Anjan Biswas
Keyword(s):  
Finite Difference ◽  
Numerical Simulations ◽  
Power Law ◽  
Soliton Solution ◽  
Bifurcation Analysis ◽  
Soliton Solutions ◽  
Phase Portraits ◽  
Zakharov Equation ◽  
Topological Soliton ◽  
Klein Gordon

This paper addresses the Klein-Gordon-Zakharov equation with power law nonlinearity in (1+1)-dimensions. The integrability aspect as well as the bifurcation analysis is studied in this paper. The numerical simulations are also given where the finite difference approach was utilized. There are a few constraint conditions that naturally evolve during the course of derivation of the soliton solutions. These constraint conditions must remain valid in order for the soliton solution to exist. For the bifurcation analysis, the phase portraits are also given.

scholarly journals Soliton Solutions of the Klein-Gordon-Zakharov Equation with Power Law Nonlinearity

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Mehmet Ekici ◽  
Durgun Duran ◽  
Abdullah Sonmezoglu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Power Law ◽  
Elliptic Function ◽  
Soliton Solutions ◽  
Mathematical Physics ◽  
Zakharov Equation ◽  
Trial Equation Method ◽  
Klein Gordon

We introduce a new version of the trial equation method for solving nonintegrable partial differential equations in mathematical physics. Some exact solutions including soliton solutions and rational and elliptic function solutions to the Klein-Gordon-Zakharov equation with power law nonlinearity in (1 + 2) dimensions are obtained by this method.

scholarly journals Analytical and Numerical Methods for the CMKdV-II Equation

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Ömer Akin ◽  
Ersin Özuğurlu
Keyword(s):  
Numerical Methods ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Iterative Method ◽  
Soliton Solution ◽  
Bilinear Form ◽  
Difference Method ◽  
Soliton Solutions ◽  
Hirota’S Bilinear Form ◽  
De Vries

Hirota's bilinear form for the Complex Modified Korteweg-de Vries-II equation (CMKdV-II) is derived. We obtain one- and two-soliton solutions analytically for the CMKdV-II. One-soliton solution of the CMKdV-II equation is obtained by using finite difference method by implementing an iterative method.

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