Slow passage through resonance.

Resonance in slow passage problem

The slow passage problem through a resonance is considered. As a model problem, we consider a damped harmonically-forced oscillator whose forcing frequency is slowly ramped linearly in time. The set-up is similar to the familiar slow passage through a Hopf bifurcation problem, where for slow variations of the control parameter, oscillations are delayed until the parameter has exceeded the criti...

Slow passage through parametric resonance for a weakly nonlinear dispersive wave ∗

A solution of the nonlinear Klein-Gordon equation perturbed by a parametric driver is studied. The frequency of the parametric perturbation varies slowly and passes through a resonant value. It yields a change in a solution. We obtain a connection formula for the asymptotic solution before and after the resonance.

Slow Passage through Resonance for a Weakly Nonlinear Dispersive Wave

On passage through resonances in volume-preserving systems.

Resonance processes are common phenomena in multiscale (slow-fast) systems. In the present paper we consider capture into resonance and scattering on resonance in 3D volume-preserving multiscale systems. We propose a general theory of those processes and apply it to a class of kinematic models inspired by viscous Taylor-Couette flows between two counter-rotating cylinders. We describe the pheno...

Resonance-induced Surfatron Acceleration of a Relativistic Particle

We study motion of a relativistic charged particle in a plane slow electromagnetic wave and background uniform magnetic field. The wave propagates normally to the background field. The motion of the particle can be described by a Hamiltonian system with two degrees of freedom. Parameters of the problem are such that in this system one can identify slow and fast variables: three variables are ch...