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Movable singularity of semi linear Heun equation and application to blowup phenomenon

  • Masafumi YoshinoEmail author
Article
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Abstract

In this paper we shall study the movable singularity of semi linear Heun equation and its application to the blowup of a semi linear wave equation. In fact, the semi linear Heun equation appears if we consider a radially symmetric self-similar solution of the semi linear wave equation. By the movable singularity we mean the singularity which does not appear in the coefficients of the equation and that depends on the respective solution. We focus on movable singularity when we construct a singular solution of the semi linear wave equation with singularities on the characteristic cone. In the proof of our theorem we reduce our equation to a simpler form by the method similar to the so-called Birkhoff reduction, then we analyze the reduced equation. The latter part is closely related with the parametrization of a solution in terms of the Jacobi elliptic function.

Keywords

Movable singularity Blowup Heun equation 

Mathematics Subject Classification

35C10 45E10 

Notes

Acknowledgements

The author would like to express sincere thanks to anonymous referee for the constructive suggestions to the paper.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsHiroshima UniversityHiroshimaJapan

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