Oscillations and Resonances

DOI10.1515/9783110335682zbMath1377.34001OpenAlexW2605852125MaRDI QIDQ2797804

S. G. Glebov, Nikolai N. Tarkhanov, Oleg M. Kiselev

Publication date: 31 March 2016

Full work available at URL: https://doi.org/10.1515/9783110335682

zbMATH Keywords

coupled oscillatorsnonlinear oscillationsasymptotic expansionsperturbed nonlinear differential equationsautoresonances in nonlinear systemssingular perturbation WKB methods

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Asymptotic expansions of solutions to ordinary differential equations (34E05) Research exposition (monographs, survey articles) pertaining to ordinary differential equations (34-02)

Related Items

Asymptotic behaviour of measure for captured trajectories into parametric autoresonance ⋮ An asymptotic structure of the bifurcation boundary of the perturbed Painlevé-2 equation ⋮ Formal Asymptotics of Parametric Subresonance ⋮ Conditions for Phase Locking and Dephasing of Autoresonant Pumping ⋮ Emergence and decay of \(\pi \)-kinks in the sine-Gordon model with high-frequency pumping ⋮ Uniform asymptotics of the elliptic sine ⋮ Bifurcations in asymptotically autonomous Hamiltonian systems under oscillatory perturbations ⋮ Resonances in asymptotically autonomous systems with a decaying chirped-frequency excitation