Adiabatic approximation for a model of cyclotron motion

DOI10.1134/S000143461705011XzbMath1381.34069OpenAlexW2666578495MaRDI QIDQ2401649

Leonid A. Kalyakin

Publication date: 4 September 2017

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s000143461705011x

zbMATH Keywords

asymptoticsadiabatic approximationresonance capture

Mathematics Subject Classification ID

Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Averaging method for ordinary differential equations (34C29) Qualitative investigation and simulation of ordinary differential equation models (34C60) Motion of charged particles (78A35) Singular perturbations for ordinary differential equations (34E15)

Cites Work

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• The separation of motions in systems with rapidly rotating phase
• Application of the method of two-scale expansions to the single-frequency problem of the theory of nonlinear oscillations
• 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
• Oscillations near a separatrix in the Duffing equation
• Asymptotic analysis of autoresonance models
• An asymptotic solution slowly crossing the separatrix near a saddle centre bifurcation point

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