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Hokkaido University Preprint Series in Mathematics >
Multivalued solutions to the eikonal equation in stratified media
| Title: | Multivalued solutions to the eikonal equation in stratified media |
| Authors: | Izumiya, S. Browse this author | | Kossioris, G. Browse this author | | Makrakis, G. Browse this author |
| Issue Date: | 1-Jul-1999 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 466 |
| Start Page: | 1 |
| End Page: | 24 |
| Abstract: | 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. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69216 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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