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Asymptotic profile of a least-energy solution to a nonlinear elliptic equation in nonlinear optics

Published online by Cambridge University Press:  14 July 2008

Masataka Shibata
Masataka Shibata
Affiliation:
Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan (shibata@math.titech.ac.jp)
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Abstract

We consider a least-energy solution to a nonlinear elliptic equation arising in a nonlinear optics model. The equation is linear in a given bounded domain $D$ and nonlinear in $\mathbb{R}^N\setminus D$. We consider a singular limiting problem to obtain a relation between a location of a spiky solution and a geometry of $D$.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 138 , Issue 3 , June 2008 , pp. 619 - 646
Copyright
2008 Royal Society of Edinburgh

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