Hewett, DP;
Ockendon, JR;
Smyshlyaev, VP;
(2019)
Contour integral solutions of the parabolic wave equation.
Wave Motion
, 84
pp. 90-109.
10.1016/j.wavemoti.2018.09.015.
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Abstract
We present a simple systematic construction and analysis of solutions of the two-dimensional parabolic wave equation that exhibit far-field localisation near certain algebraic plane curves. Our solutions are complex contour integral superpositions of elementary plane wave solutions with polynomial phase, the desired localisation being associated with the coalescence of saddle points. Our solutions provide a unified framework in which to describe some classical phenomena in two-dimensional high frequency wave propagation, including smooth and cusped caustics, whispering gallery and creeping waves, and tangent ray diffraction by a smooth boundary. We also study a subclass of solutions exhibiting localisation near a cubic parabola, and discuss their possible relevance to the study of the canonical inflection point problem governing the transition from whispering gallery waves to creeping waves.
| Type: | Article |
|---|---|
| Title: | Contour integral solutions of the parabolic wave equation |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.wavemoti.2018.09.015 |
| Publisher version: | https://doi.org/10.1016/j.wavemoti.2018.09.015 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Parabolic wave equation, Paraxial approximation, Canonical inflection point problem |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10061837 |
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