Skip to main content
Log in

Propagation in the earth-ionosphere waveguide by the multiscaling method

  • Published:
Journal of Engineering Mathematics Aims and scope Submit manuscript

Summary

A problem of propagation of modulated high-frequency signals in a waveguide of nonconstant height and nonconstant wall impedance is analysed. A multiple-scale method is used, which reduces the three-dimensional problem to a twodimensional problem for each mode. The modal propagation problem is analysed by the ray method, giving rise to phase and group velocities, and showing the possibility of focusing effects due to variation in height and wall impedance. Mode coupling effects are shown and mode coupling coefficients calculated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. B. Rulf,The Signalling Problem in General Waveguides, to be published.

  2. B. Rulf,Acoustic Propagation in Ducts, to be published.

  3. B. Robinson,Ph.D. dissertation (unpublished), Tel Aviv University, 1972.

  4. B. Rulf, An Asymptotic Theory of Guided Waves,Jour. Engineering Math., 4 (3) (1970).

  5. D. Hector, J. Cohen and N. Bleistein, Ray Method Expansions for Surface and Internal Waves in Inhomogeneous Oceans of Variable Depth.Stud. Appl. Math. LI (2), 121–137 (1972).

    MathSciNet  Google Scholar 

  6. R. Courant and D. Hilbert,Methods of Mathematical Physics, Vol. 2, Interscience, New York, (1962).

    Google Scholar 

  7. M. Kline and I. W. Kay,Electromagnetic Theory and Geometrical Optics, Interscience, New York, 1965.

    Google Scholar 

  8. R. M. Lewis and J. B. Keller,Asymptotic Methods for Partial Differential Equations, N. Y. U. Research Report EM-194 (1964).

  9. D. Ludwig, Uniform Asymptotic Expansions of Wave Propagations and Diffraction Problem,SIAM Rev., 12, 325–331, (1970). See also bibliography here.

    Article  MATH  MathSciNet  Google Scholar 

  10. A. H. Nayfeh,Perturbation Methods, John Wiley, New York (1973).

    Google Scholar 

  11. L. A. Segel, Simplification and Scaling,SIAM Rev., 14 (4), 547–571 (1972).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This work was done while the author was visiting at the Department of Mathematics, Rensselaer Polytechnic Institute, Troy, New York, and was supported by NSF Grant No. GU 2605.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rulf, B. Propagation in the earth-ionosphere waveguide by the multiscaling method. J Eng Math 8, 141–148 (1974). https://doi.org/10.1007/BF02353616

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02353616

Keywords

Navigation