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Seminars in mathematics

Mathematical Problems in Wave Propagation Theory

Editors: Babich, V. M. (Ed.)

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About this book

The papers comprising this collection are directly or indirectly related to an important branch of mathematical physics - the mathematical theory of wave propagation and diffraction. The paper by V. M. Babich is concerned with the application of the parabolic-equation method (of Academician V. A. Fok and M. A, Leontovich) to the problem of the asymptotic behavior of eigenfunc­ tions concentrated in a neighborhood of a closed geodesie in a Riemannian space. The techniques used in this paper have been föund useful in solving certain problems in the theory of open resonators. The topic of G. P. Astrakhantsev's paper is similar to that of the paper by V. M. Babich. Here also the parabolic-equation method is used to find the asymptotic solution of the elasticity equations which describes Love waves concentrated in a neighborhood of some surface ray. The paper of T. F. Pankratova is concerned with finding the asymptotic behavior of th~ eigenfunc­ tions of the Laplace operator from the exact solution for the surface of a triaxial ellipsoid and the re­ gion exterior to it. The first three papers of B. G. Nikolaev are somewhat apart from the central theme of the col­ lection; they treat the integral transforms with respect to associated Legendre functions of first kind and their applications. Examples of such applications are the use of this transform for the solution of integral equations with symmetrie kernels and for the solution of certain problems in the theory of electrical prospecting.

Table of contents (10 chapters)

Table of contents (10 chapters)
  • Sharply Directed Propagation of Love-Type Surface Waves

    Pages 1-5

    Astrakhantsev, G. P.

  • Eigenfunctions Concentrated in a Neighborhood of a Closed Geodesic

    Pages 7-26

    Babich, V. M.

  • The Calculation of Interference Waves for Diffraction by a Cylinder and a Sphere

    Pages 27-44

    Lanin, A. I.

  • The Expansion of an Arbitrary Function in Terms of an Integral of Associated Legendre Functions of First Kind with Complex Index

    Pages 45-51

    Nikolaev, B. G.

  • Application of an Integral Transform with Generalized Legendre Kernel to the Solution of Integral Equations with Symmetric Kernels

    Pages 53-56

    Nikolaev, B. G.

Buy this book

eBook $84.99
price for USA in USD
  • ISBN 978-1-4757-0334-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $109.99
price for USA in USD
  • ISBN 978-1-4757-0336-8
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Mathematical Problems in Wave Propagation Theory
Editors
  • V. M. Babich
Series Title
Seminars in mathematics
Series Volume
9
Copyright
1970
Publisher
Springer US
Copyright Holder
Consultants Bureau, New York
eBook ISBN
978-1-4757-0334-4
DOI
10.1007/978-1-4757-0334-4
Softcover ISBN
978-1-4757-0336-8
Edition Number
1
Number of Pages
VII, 107
Topics