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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2011, Volume 51, Number 8, Pages 1419–1433 (Mi zvmmf9523)  
This article is cited in 2 scientific papers (total in 2 papers)

Cauchy problem for the Mathieu equation away from parametric resonance

A. F. Kurin

Faculty of Physics, Voronezh State University, Universitetskaya pl. 1, Voronezh, 394006 Russia
Full-text PDF (796 kB) Citations (2)
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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.
Key words: Cauchy problem, Mathieu equation, averaging method, amplitude, phase.
Received: 05.04.2010
English version:
Computational Mathematics and Mathematical Physics, 2011, Volume 51, Issue 8, Pages 1325–1338
DOI: https://doi.org/10.1134/S0965542511080136
Bibliographic databases:
Document Type: Article
UDC: 519.624.2
Language: Russian
Citation: A. F. Kurin, “Cauchy problem for the Mathieu equation away from parametric resonance”, Zh. Vychisl. Mat. Mat. Fiz., 51:8 (2011), 1419–1433; Comput. Math. Math. Phys., 51:8 (2011), 1325–1338
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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