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  - Garifullinevich, Rustem Nail
A1  - Suleimanov, Bulat Irekovich
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Phase shift in the Whitham zone for the Gurevich-Pitaevskii special solution of the Korteweg-de Vries equation
N2  - We get the leading term of the Gurevich-Pitaevskii special solution of the KdV equation in the oscillation zone without using averaging methods.
Y1  - 2010
UR  - http://www.sciencedirect.com/science/journal/03759601
U6  - https://doi.org/10.1016/j.physleta.2010.01.057
SN  - 0375-9601
ER  - 
TY  - JOUR
A1  - Stepanenko, Victor
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - The Cauchy problem for Chaplygin's system
N2  - 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.
Y1  - 2010
UR  - http://www.informaworld.com/openurl?genre=journal&issn=1747-6933
U6  - https://doi.org/10.1080/17476930903394978
SN  - 1747-6933
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  -