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Singular solitons and bifurcation analysis of quadratic nonlinear Klein-Gordon equation. (English) Zbl 1269.35006
Summary: This paper studies the Klein-Gordon equation with quadratic nonlinearity. The ansatz approach is used to first obtain the singular soliton solution of the equation along with the corresponding domain restriction. The birfurcation analysis is also carried out. By this analysis, a few more traveling wave solutions are retrieved. The bifurcation phase portraits are also given.

MSC:
35C07 Traveling wave solutions
35B32 Bifurcations in context of PDEs
35C08 Soliton solutions
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