@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{GarifullinevichSuleimanovTarkhanov2010,
  author    = {Garifullinevich, Rustem Nail and Suleimanov, Bulat Irekovich and Tarkhanov, Nikolai Nikolaevich},
  title     = {Phase shift in the Whitham zone for the Gurevich-Pitaevskii special solution of the Korteweg-de Vries equation},
  issn      = {0375-9601},
  doi       = {10.1016/j.physleta.2010.01.057},
  year      = {2010},
  abstract  = {We get the leading term of the Gurevich-Pitaevskii special solution of the KdV equation in the oscillation zone without using averaging methods.},
  language  = {en}
}
@article{StepanenkoTarkhanov2010,
  author    = {Stepanenko, Victor and Tarkhanov, Nikolai Nikolaevich},
  title     = {The Cauchy problem for Chaplygin's system},
  issn      = {1747-6933},
  doi       = {10.1080/17476930903394978},
  year      = {2010},
  abstract  = {We discuss the Cauchy problem for the so-called Chaplygin system which often appears in gas, aero- and hydrodynamics. This system can be thought of as a nonlinear analogue of the Cauchy-Riemann system in the plane. We pose Cauchy data on a part of the boundary and apply variational approach to construct a solution to this ill-posed problem. The problem actually gives insight to fundamental questions related to instable problems for nonlinear equations.},
  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}
}