@article{GlebovKiselevTarkhanov2010,
  author    = {Glebov, Sergei and Kiselev, Oleg and Tarkhanov, Nikolai Nikolaevich},
  title     = {Autoresonance in a dissipative system},
  issn      = {1751-8113},
  doi       = {10.1088/1751-8113/43/21/215203},
  year      = {2010},
  abstract  = {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.},
  language  = {en}
}
@article{GlebovKiselevTarkhanov2010,
  author    = {Glebov, Sergei and Kiselev, Oleg and Tarkhanov, Nikolai Nikolaevich},
  title     = {Weakly nonlinear dispersive waves under parametric resonance perturbation},
  issn      = {0022-2526},
  doi       = {10.1111/j.1467-9590.2009.00460.x},
  year      = {2010},
  abstract  = {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.},
  language  = {en}
}