Details

Autor(en) / Beteiligte

• Babich, V. M

Titel

Mathematical Problems in Wave Propagation Theory [Elektronische Ressource]

Ist Teil von

• Seminars in Mathematics : 9

Ort / Verlag

Boston, MA : Springer US

Erscheinungsjahr

1970

Link zu anderen Inhalten

• Volltext

Beschreibungen/Notizen

• 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 eigenfunctions 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~ eigenfunctions of the Laplace operator from the exact solution for the surface of a triaxial ellipsoid and the region exterior to it. The first three papers of B. G. Nikolaev are somewhat apart from the central theme of the collection; 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