In this work we show that the capture into parametric resonance may be explained as the pitchfork bifurcation in the primary para-metric resonance equation. We prove that the solution close to theâ€¦ (More)

We consider a resonantly perturbed system of coupled nonlinear oscillators with small dissipation and outer periodic perturbation. We show that for the large time tâˆ¼É›(-2) one component of the systemâ€¦ (More)

We study a hard regime of stimulation of two-frequency oscillations in the main resonance equation with a fast oscillating external force: ÎµiÏˆ â€² + |Ïˆ| 2 Ïˆ = exp (it 2 /(2Îµ)), 0 < Îµ â‰ª 1. Thisâ€¦ (More)

We investigate a propagation of solitons for nonlinear SchrÃ¶dinger equation under small driving force. The driving force passes through the resonance. The process of scattering on the resonance leadsâ€¦ (More)

Solution of the nonlinear Klein-Gordon equation perturbed by small external force is investigated. The perturbation is represented by finite collections of harmonics. The frequencies of theâ€¦ (More)

We study an initial stage of autoresonant growth of a solution in a dissipative system. We construct an asymptotic formula of an autoresonant germ that is an attractor for autoresonant solutions. Weâ€¦ (More)

Solution of the nonlinear Klein-Gordon equation perturbed by small external force is investigated. The frequency of perturbation varies slowly and passes through a resonance. The resonance generatesâ€¦ (More)

We investigate a system of two weakly coupled oscillators. It is shown that an external periodic perturbation can lead to the capture into resonance. Asymptotic description and numerical simulationsâ€¦ (More)

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. Itâ€¦ (More)