Parametric resonance in adiabatic oscillators

DOI10.1007/s00025-010-0043-3zbMath1216.34027OpenAlexW2022399101MaRDI QIDQ708721

Pavel Nesterov, Vladimir S. Burd

Publication date: 14 October 2010

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-010-0043-3

zbMATH Keywords

method of averagingasymptotic integrationparametric resonanceadiabatic oscillatoroscillatory decreasing coefficientsLevinson's fundamental theorem

Mathematics Subject Classification ID

Linear ordinary differential equations and systems (34A30) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Averaging method for ordinary differential equations (34C29) Growth and boundedness of solutions to ordinary differential equations (34C11) Asymptotic properties of solutions to ordinary differential equations (34D05) Parametric resonances in linear vibration theory (70J40)

Related Items (10)

Capture into resonance in nonlinear oscillatory systems with decaying perturbations ⋮ Asymptotic integration of functional differential systems with oscillatory decreasing coefficients ⋮ Appearance of new parametric resonances in time-dependent harmonic oscillator ⋮ Zeroes of the spectral density of discrete Schrödinger operator with Wigner-von Neumann potential ⋮ Asymptotic analysis of systems with damped oscillatory perturbations ⋮ Decaying oscillatory perturbations of Hamiltonian systems in the plane ⋮ On eigenvalues of the one-dimensional Dirac operator with oscillatory decreasing potential ⋮ Bifurcations in asymptotically autonomous Hamiltonian systems under oscillatory perturbations ⋮ Resonances in asymptotically autonomous systems with a decaying chirped-frequency excitation ⋮ Asymptotic integration of certain Volterra integro-differential equations with oscillatory decreasing kernels

Cites Work

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• The asymptotic nature of solutions of linear systems of differential equations
• The asymptotic solution of second-order differential equations
• Justification of Asymptotic Formulas for the Fourth Painlevé Equation
• Asymptotic Integrations of the Adiabatic Oscillator
• The Adiabatic Linear Oscillator

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