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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
