Advertisement

Green’s Function of Wave Equation for Inhomogeneous Medium

  • Evgueni G. Saltykov

Abstract

A method is proposed for constructing the Green’s function for the wave equation describing wave propagation in the ionosphere with electronic density N(z,x) depending on two independent variables. By means of the Fourier transform with respect to t, we obtain a reduced wave equation with an inhomo-geneous term of the δ-function type. The last problem solution has the form of integral containing the eigenfunctions of one-dimensional problem. The eigenfunctions depend on the parameter x. The expansion coefficients satisfy the second kind integral equation. In the weak dependence case of electronic density on a coordinate x, the integral equation can be solved by the successive approximations method.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    B. M. Levitan, “Inverse Sturm-Liouville’s Problems,” Nauka, Moscow (1984).Google Scholar
  2. 2.
    A. Sommerfeld, “Partielle Differentialgleichungen der Physik,” Akademische Verlagsgesellschaft Geest & Portig K.-G., Leipzig (1966).Google Scholar
  3. 3.
    M. V. Fedorük, “Asymptotic Expansion Integrals and Series,” Nauka, Moscow (1987).Google Scholar
  4. 4.
    N. Danford and J. T. Shwartz, “Linear Operators,” Part 2, Interscience Publishers, New York, London (1963).Google Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Evgueni G. Saltykov
    • 1
  1. 1.Department of Computational Math, and CyberneticsMoscow State UniversityMoscowUSSR

Personalised recommendations