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

Abstract

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.