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Reduction of the Mathieu equation to a nonlinear equation of the first order

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Moscow University Mechanics Bulletin Aims and scope

Abstract

A second order equation with periodic coefficients is considered. It is shown that its analysis can be reduced to the study of a nonlinear equation of the first order. The second approximation is obtained for the first resonance region of the Mathieu equation. This approximation describes the behavior of solutions inside this resonance region and near it.

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Authors and Affiliations

  1. Moscow State University, Moscow University Institute of Mechanics, Leninskie Gory, Moscow, 119991, Russia

    V. M. Budanov

Authors
  1. V. M. Budanov
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Correspondence to V. M. Budanov.

Additional information

Original Russian Text © V.M. Budanov, 2016, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2016, Vol. 71, No. 4, pp. 66–69.

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Budanov, V.M. Reduction of the Mathieu equation to a nonlinear equation of the first order. Moscow Univ. Mech. Bull. 71, 98–101 (2016). https://doi.org/10.3103/S0027133016040051

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  • DOI: https://doi.org/10.3103/S0027133016040051

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