Abstract
This work researches the singular traveling wave system of the ( $$\hbox {n}+1$$ )-dimensional nonlinear Klein-Gordon equation via the bifurcation theory of dynamical systems. The bifurcations and phase portraits of the traveling wave system are investigated and the influence of singularity and nonlinearity on the dynamical behavior of traveling wave solutions is discussed. Accordingly the various sufficient conditions for the existence of analytic and nonanalytic traveling wave solutions are obtained. Furthermore some exact solutions are given to illustrate the results.
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