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Cauchy problem for the Mathieu equation away from parametric resonance

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Abstract

Four solutions of the Cauchy problem for Mathieu’s equation away from parametric resonance domains are analytically constructed using an asymptotic averaging method in the fourth approximation. Three solutions occur near fractional parameter values at which slow combination phases exist. The fourth solution occurs in the absence of slow phases away from parametric resonance domains and the fractional parameter values.

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Authors and Affiliations

  1. Faculty of Physics, Voronezh State University, Universitetskaya pl. 1, Voronezh, 394006, Russia

    A. F. Kurin

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  1. A. F. Kurin
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Correspondence to A. F. Kurin.

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Original Russian Text © A.F. Kurin, 2011, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2011, Vol. 51, No. 8, pp. 1419–1433.

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Kurin, A.F. Cauchy problem for the Mathieu equation away from parametric resonance. Comput. Math. and Math. Phys. 51, 1325–1338 (2011). https://doi.org/10.1134/S0965542511080136

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  • DOI: https://doi.org/10.1134/S0965542511080136

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