Ukrainian Mathematical Journal

, Volume 45, Issue 6, pp 871–883 | Cite as

Scattering matrix for the wave equation with finite radial potential in the two-dimensional space

  • A. L. Mil'man


Expressions for partial scattering matricesSl(λ) are obtained for all naturall by using Adamyan's result, which establishes a universal relationship between the scattering matrix for the wave equation with finite potential in a even-dimensional space and the characteristic operator function of a special contraction operator, which describes the dissipation of energy from the region of the space containing a scatterer. It is shown that this problem can be reduced to the case ofl=0 for all evenl and to the case ofl=1 for all oddl.


Characteristic Operator Wave Equation Operator Function Contraction Operator Special Contraction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    P. Lax and R. S. Phillips,Scattering Theory, Academic Press, New York (1967).Google Scholar
  2. 2.
    P. Lax and R. S. Phillips, “Scattering theory for the acoustic equation in an even number of space dimensions,”Indiana Univ. Math. J.,22, 101–134 (1972).Google Scholar
  3. 3.
    V. M. Adamyan and D. Z. Arov, “On scattering operators and semigroups of contractions in the Hilbert space,”Dokl. Akad. Nauk SSSR,165, No. 1, 9–12 (1965).Google Scholar
  4. 4.
    V. M. Adamyan, “On scattering theory for the wave equations in even-dimensional spaces,”Funkts. Anal. Prilozh.,10, No. 4, 1–8 (1976).Google Scholar
  5. 5.
    A. L. Mil'man, “The inverse problem in the acoustic scattering theory for centrally symmetric finite obstacles in the two-dimensional space,”Ukr. Mat. Zh.,42, No. 12, 1649–1657 (1990).Google Scholar
  6. 6.
    B. Szökefalvy-Nagy and C. Foias,Analyse Harmonique des Opérateurs de l'Espace de Hilbert, Académiai Kiadô, Paris (1967).Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • A. L. Mil'man
    • 1
  1. 1.NPO “Kol'tso”Odessa

Personalised recommendations