Painlevé II equation as a model of a resonant interaction of oscillators

DOI10.1134/S0081543818090134zbMath1418.34083OpenAlexW2921676174MaRDI QIDQ2424186

Leonid A. Kalyakin

Publication date: 24 June 2019

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0081543818090134

zbMATH Keywords

asymptoticsoscillationsmall parameternonlinear equationresonance

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Nonlinear resonances for nonlinear problems in mechanics (70K30)

Related Items (1)

Resonance capture in a system of two oscillators near equilibrium

Cites Work

• Asymptotic expressions for the second Painlevé functions
• The separation of motions in systems with rapidly rotating phase
• Averaging in the autoresonance model
• The second Painlevé equation as a model for the electric field in a semiconductor.
• Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro.
• Asymptotic analysis of autoresonance models
• Averaging, passage through resonances, and capture into resonance in two-frequency systems
• SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS
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