Dynamics of Partial Differential Equations

Volume 2 (2005)

Number 3

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

Pages: 261 – 280

DOI: https://dx.doi.org/10.4310/DPDE.2005.v2.n3.a2


Sergei Glebov (Ufa State Petroleum Technical University, Russia)

Oleg Kiselev (Institute of Mathematics, USC RAS, Russia)


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.


Klein-Gordon equation, wave packets, finite collections of harmonics, asymptotics, resonance

2010 Mathematics Subject Classification

Primary 35-xx. Secondary 78-xx.

Published 1 January 2005