Reduction of the Mathieu Equation to a Nonlinear Equation of the First Order

V. M. Budanov

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Reduction of the Mathieu Equation to a Nonlinear Equation of the First Order

机译：将Mathieu方程简化为一阶非线性方程

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摘要

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.

机译：考虑具有周期系数的二阶方程。结果表明，它的分析可以简化为一阶非线性方程的研究。对于Mathieu方程的第一共振区域获得第二近似值。这种近似描述了共振区域内部及其附近溶液的行为。

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《Moscow university mechanics bulletin》 |2016年第4期|98-101|共4页
作者
V. M. Budanov;
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Moscow State University, Moscow University Institute of Mechanics,Leninskie Gory, Moscow, 119991, Russia;

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Reduction of the Mathieu Equation to a Nonlinear Equation of the First Order

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