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Abstract

In this paper we analyze movable singularities of the solutions of the equation for self-similar profiles resulting from semilinear wave equation. We study local analytic solutions around two fixed singularity points of this equation—$\rho=0$ and $\rho=1$. The movable singularities of local analytic solutions at the origin will be connected with those of the Lane–Emden equation. The function describing approximately their position on the complex plane will be derived. For $\rho>1$ some topological considerations will be presented that describe movable singularity of local analytic solution at $\rho=1$. Numerical illustrations of the results will also be provided.