Justification of an asymptotic expansion at infinity
A family of asymptotic solutions at infinity for the system of ordinary differential equations is considered. Existence of exact solutions which have these asymptotics is proved.
math.CA↗
arXiv subjects
L. A. Kalyakin
Publications and source records attributed to L. A. Kalyakin.
Averaging of an autoresonance model
Autoresonance is a phase locking phenomenon occurring in nonlinear oscislatory system, which is forced by oscillating perturbation. Many physical applicatcons of the autoresonance are known in nonlenear physics. The essence of the phenomecon is that the nonlinear oscillator selfadjusts to the varying external conditions so that it remains in resonance with the orivvr for a long time. This long time resonance leads to a strong increase in the response amplitude under weak drivinc perturbation. An analytic treatment of a simple mathematical model is done here by means of asymptotic analysis using a small driving parameter. The main result is finding threshold for entering the autoresonance.
nlin.AO↗
Asymptotic analysis of a model of autoresonance
Autoresonance is a phase locking phenomenon occurring in nonlinear oscillatory system, which is forced by oscillating perturbation. Many physical applications of the autoresonance are known in nonlinear physics. The essence of the phenomenon is that the nonlinear oscillator selfadjusts to the varying external conditions so that it remains in resonance with the driver for a long time. This long time resonance leads to a strong increase in the response amplitude under weak driving perturbation. An analytic treatment of a simple mathematical model is done here by means of asymptotic analysis using a small driving parameter. The main result is finding threshold for entering the autoresonance.
nlin.AO↗
Singular solution of the Liouville equation under perturbation
Small perturbation of the Liouville equation under singular initial data is considered. An asymptotics of the singular solution is constructed by the method which is similar to Bogolubov -- Krylov one. The main object is an asymptotics of the singular lines.
solv-int↗
Liouville equation under perturbation
Small perturbation of the Liouville equation under smooth initial data is considered. Asymptotic solution which is available for a long time interval is constructed by the two scale method.
solv-int↗