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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2011 Volume 51, Number 8, Pages 1419–1433 (Mi zvmmf9523)

This article is cited 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

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.

UDC: 519.624.2

Received: 05.04.2010


 English version:
Computational Mathematics and Mathematical Physics, 2011, 51:8, 1325–1338

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© Steklov Math. Inst. of RAS, 2026