TY  - JOUR
A1  - Glebov, Sergei
A1  - Kiselev, Oleg
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Autoresonance in a dissipative system
N2  - We study the autoresonant solution of Duffing's equation in the presence of dissipation. This solution is proved to be an attracting set. We evaluate the maximal amplitude of the autoresonant solution and the time of transition from autoresonant growth of the amplitude to the mode of fast oscillations. Analytical results are illustrated by numerical simulations.
Y1  - 2010
UR  - http://iopscience.iop.org/1751-8121/
U6  - https://doi.org/10.1088/1751-8113/43/21/215203
SN  - 1751-8113
ER  - 
TY  - JOUR
A1  - Glebov, Sergei
A1  - Kiselev, Oleg
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Weakly nonlinear dispersive waves under parametric resonance perturbation
N2  - We consider a solution of the nonlinear Klein-Gordon equation perturbed by a parametric driver. The frequency of parametric perturbation varies slowly and passes through a resonant value, which leads to a solution change. We obtain a new connection formula for the asymptotic solution before and after the resonance.
Y1  - 2010
UR  - http://www3.interscience.wiley.com/cgi-bin/issn?DESCRIPTOR=PRINTISSN&VALUE=0022-2526
U6  - https://doi.org/10.1111/j.1467-9590.2009.00460.x
SN  - 0022-2526
ER  -