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S. G. Glebov

Publications and source records attributed to S. G. Glebov.

5 recordsLinked to original sources
arXiv2005

The slowly passage through the resonances and wave packets with the different carriers

Solution of the nonlinear Klein-Gordon equation perturbed by small external force is investigated. The perturbation is represented by finite collections of harmonics. The frequencies of the perturbation vary slowly and pass through the resonant values consecutively. The resonances lead to the sequence of the wave packets with the different fast oscillated carriers. Full asymptotic description of this process is presented.

math-ph↗
arXiv2004

Scattering of solitons on resonance. Asymptotics and numeric simulations

We investigate a propagation of solitons for nonlinear Schrödinger equation under small driving force. The driving force passes through the resonance. The process of scattering on the resonance leads to changing of number of solitons. After the resonance the number of solitons depends on the amplitude of the driving force. The analytical results were obtained by WKB and matching method. We bring two examples of numeric simulations for verifying obtained analytical formulas.

nlin.PS↗
arXiv2001

Asymptotic description of nonlinear resonance

We study a hard regime of stimulation of two-frequency oscillations in the main resonance equation with a fast oscillating external force: $ \ve i ψ' + |ψ|^2ψ= \exp\big(it^2/ (2\ve)\big), 0<\ve\ll1$. This phenomenon is caused by resonance between an eigenmode and the external force. The asymptotic solution before, inside and after the resonance layer is studied in detail and matched.

math.DS↗