Adiabatic approximation in a resonance capture problem

DOI10.13108/2017-9-3-61zbMath1463.34217OpenAlexW2780890293MaRDI QIDQ5136707

Leonid A. Kalyakin

Publication date: 27 November 2020

Published in: Ufimskii Matematicheskii Zhurnal (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/ufa387

zbMATH Keywords

asymptoticssmall parameternonlinear oscillationsadiabatic approximationcapture into resonance

Mathematics Subject Classification ID

Averaging method for ordinary differential equations (34C29) Asymptotic properties of solutions to ordinary differential equations (34D05) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Nonlinear resonances for nonlinear problems in mechanics (70K30)

Cites Work

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• Asymptotic analysis of an autoresonance model
• Passage through a separatrix in a resonance problem with a slowly-varying parameter
• Captures into resonance and scattering on resonance in dynamics of a charged relativistic particle in magnetic field and electrostatic wave
• Averaging for Hamiltonian systems with one fast phase and small amplitudes
• Asymptotic analysis of the model of gyromagnetic autoresonance
• Asymptotic behavior of solutions of equations of main resonance
• Asymptotic analysis of autoresonance models
• An asymptotic solution slowly crossing the separatrix near a saddle centre bifurcation point
• Boundary of the Basin of Attraction for Weakly Damped Primary Resonance

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