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Synopsis
Explore how high-frequency methods reveal the behavior of wave diffraction.
This book explains a practical asymptotic approach to solving boundary-value problems for waves, focusing on how solutions behave as frequency grows large. The leading term matches the familiar geometrical-optics picture, while the method directly builds the full asymptotic expansion without needing exact solutions.
The text presents a clear formulation of the method, then applies it to a range of diffraction problems. It shows how to derive recursive equations along ray paths and how energy conservation emerges in narrow ray tubes. Several canonical geometries are treated, highlighting when the approach gives complete results and when additional techniques are needed for diffracted rays. The work also discusses connections to Maxwell’s and Schrödinger-type problems, and compares asymptotic results with exact solutions where available.- Learn how to set up an asymptotic expansion for u as frequency grows, and how to interpret the phase and amplitude along rays.
- See step-by-step how to derive the eikonal and transport equations that underpin geometrical optics.
- Review multiple classic diffraction scenarios, including plane and spherical waves, and waves near curved boundaries.
- Understand when the method provides complete answers and when auxiliary methods are required for diffracted components.
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Asymptotic Solution of Some Diffraction Problems (Classic Reprint)
Print on DemandSeller: Forgotten Books, London, United Kingdom
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Paperback. Condition: New. Print on Demand. This insightful book presents a thorough exploration of the asymptotic expansion of solutions to elliptic equations. The author, a renowned expert in the field, provides a comprehensive examination of cylindrical, spherical, and plane wave solutions, offering a systematic approach to understanding wave diffraction. This book fills a significant gap in the literature, as few resources have previously addressed the subject in such depth. The author meticulously explains the method of asymptotic expansion, guiding readers through the derivation of asymptotic solutions and demonstrating their application to various boundary-value problems. This book also delves into the intriguing phenomenon of diffracted rays, shedding light on their behavior and characteristics. Overall, this book serves as an invaluable resource for researchers and scholars working in the field of mathematical physics, particularly those interested in wave diffraction phenomena. Its in-depth analysis and clear explanations make it an indispensable tool for advancing the understanding of wave propagation and diffraction. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781332588695_0
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Asymptotic Solution of Some Diffraction Problems Classic Reprint
Seller: PBShop.store US, Wood Dale, IL, U.S.A.
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332588695
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Asymptotic Solution of Some Diffraction Problems Classic Reprint
Seller: PBShop.store UK, Fairford, GLOS, United Kingdom
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332588695
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