Multivalued solutions to the eikonal equation in stratified media

Izumiya, S.; Kossioris, G.; Makrakis, G.

Hokkaido University Preprint Series in Mathematics, 1999, 466, 1-24

Permalink : https://doi.org/10.14943/83612

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アクセス権	open access
DOI	https://doi.org/10.14943/83612
URI	https://hdl.handle.net/2115/69216
タイトル	Multivalued solutions to the eikonal equation in stratified media
著者	Izumiya, S. ; Kossioris, G. ; Makrakis, G.
著者名 Izumiya, S.
著者名 Kossioris, G.
著者名 Makrakis, G.
言語	英語
発行日	1999-07-01
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	466
ページ	1-24
抄録	In the present paper we study the geometric properties of the multivalued solutions to the eikonal equation and we give the appropriate classification theorems. Our motivation stems from geometrical optics for approximating high frequency waves in stratified media. We consider the case of a fixed Hamiltonian imposed by the medium, and we present the geometric framework that describes the geometric solutions, using the notion of Legendrian immersions with an initial point source or an initial smooth front. · Then, we study the singularities of the solutions in the case of a smooth or piecewise Hamiltonian in a boundaryless stratified medium. Finally, we study the singularities of the solutions in a domain with a boundary that describes the propagating field in a waveguide.
資源タイプ	紀要論文
出版タイプ	Version of Record