Abstract
A uniform asymptotic expansion for integrals of the type ʃ +∞ -∞ u ½ F ( u ) exp {i kψ ( u )}d u has been obtained in terms of generalized Airy functions, which are the solutions of the equation V"( z )+ z 2 V ( z ) = 0. This result is applied to the construction of a uniform asymptotic representation of a solution of the wave equation in the case of reflexion of a spherical wave from a plane boundary in a region including a critical ray. This asymptotic series may be divided into two series corresponding to reflected and head waves respectively, which are transformed into the ray series for these waves far from the critical ray and reduced to the expressions given by Brekhovskikh (1960) in the vicinity of the critical ray.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
Disclaimer: 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.