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Journal of Mathematical Sciences

, Volume 91, Issue 2, pp 2725–2732 | Cite as

Solutions of the membrane equation concentrated near extremal loops

  • A. S. Golubeva
Article
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Abstract

Formal asymptotic solutions of the equation\(\Delta ^2 u - \frac{{\omega ^4 }}{{c^4 \left( {x,y} \right)}}u = 0\) concentrated in the vicinity of an extremal loop with N vertices are constructed by applying the complex version of the ray method. Bibliography: 5 titles.

Keywords

Gaussian Beam Helmholtz Equation Homogeneous Problem Monodromy Operator Floquet Exponent 
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.

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References

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    I. M. Babakov,Theory of Oscillations [in Russian], Moscow (1968).Google Scholar
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    V. M. Babie and V. S. Buldyrev,Short-Wavelength Diffraction Theory, Springer-Verlag, Berlin (1991).Google Scholar
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    M. M. Popov, “Asymptotics of certain subsequences of eigenvalues of boundary-value problems for the Helmholtz equation in the multidimensional case,”Dokl. Akad. Nauk SSSR,184, 1076–1097 (1969).MATHGoogle Scholar
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    V. E. Nomofilov, “Asymptotic solutions of systems of second-order equations concentrated near a ray,”Zap. Nauchn. Semin. LOMI,104, 170–179 (1981).MATHMathSciNetGoogle Scholar
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    P. K. Rashevskii,Lectures on Differential Geometry [in Russian], Gostekhizdat (1956).Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • A. S. Golubeva

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