Bifurcation Analysis and Implicit Solution of Klein-Gordon Equation with Dual-power Law Nonlinearity in Relativistic Quantum Mechanics

Abstract This paper focuses on the nonlinear Klein-Gordon equation with dual power law nonlinearity. The traveling wave hypothesis reveals an implicit solution in terms of Gauss' hypergeometric functions. The bifurcation analysis is subsequently carried out that gives an additional set of solutions. The phase portraits of the solutions are also given.