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Dynamical Behavior of Singular Traveling Waves of (\(\hbox {n}+1\))-Dimensional Nonlinear Klein-Gordon Equation

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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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Acknowledgements

The authors sincerely thank the reviewers and editors for their valuable comments and suggestions. This research is supported by National Natural Science Foundation of China (Nos. 11662001, 11461021, 11571318, 11761019), Guangxi Natural Science Foundation (No. 2015GXNSFBA139004) and the Training Program for High Level Innovative Talents of Guizhou Province (No. QKH[2017]5658).

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Correspondence to Dahe Feng.

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Feng, D., Li, J. & Jiao, J. Dynamical Behavior of Singular Traveling Waves of (\(\hbox {n}+1\))-Dimensional Nonlinear Klein-Gordon Equation. Qual. Theory Dyn. Syst. 18, 265–287 (2019). https://doi.org/10.1007/s12346-018-0285-0

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