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- ρ = 0 and ρ = 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 ρ > 1 some topological considerations will be presented that describe movable singularity of local analytic solution at ρ = 1. Numerical illustrations of the results will also be provided.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc97-0-4,
author = {Rados\l aw A. Kycia},
title = {On movable singularities of self-similar solutions of semilinear wave equations},
journal = {Banach Center Publications},
volume = {97},
year = {2012},
pages = {59-72},
zbl = {1268.34184},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc97-0-4}
}
Radosław A. Kycia. On movable singularities of self-similar solutions of semilinear wave equations. Banach Center Publications, Tome 97 (2012) pp. 59-72. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc97-0-4/