Mathematical problems of nonlinearity

Formal Asymptotics of Parametric Subresonance

P. Astafyeva^a, O. Kiselev<sup>b

a</sup> Institute of Mathematics with Computer Centre of UFRC RAS, Ufa State Petroleum Technological University, ul. Kosmonavtov 1, Ufa, 450062 Russia
^b Innopolis University, Institute of Mathematics with Computer Centre of UFRC RAS, ul. Universitetskaya 1, Innopolis, 420500 Russia

Abstract: The article is devoted to a comprehensive study of linear equations of the second order with an almost periodic coefficient. Using an asymptotic approach, the system of equations for parametric subresonant growth of the amplitude of oscillations is obtained. Moreover, the time of a turning point from the growth of the amplitude to the bounded oscillations in the slow variable is found. Also, a comparison between the asymptotic approximation for the turning time and the numerical one is shown.

Keywords: classical analysis and ODEs, subresonant, almost periodic function,small denominator.

Received: 15.09.2022
Accepted: 05.12.2022

Language: English

DOI: 10.20537/nd221220

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