This article is cited in 9 papers

Breather resonant phase locking by an external perturbation

E. M. Maslov^a, L. A. Kalyakin^b, A. G. Shagalov<sup>c

a</sup> Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation
^b Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
^c Institute of Metal Physics, Ural Division of the Russian Academy of Sciences

Abstract: We study the effect of the resonant phase locking in the problem of the sine-Gordon equation breather under the action of a small oscillating external force with slowly varying frequency. We obtain equations determining the time evolution of the parameters of the perturbed breather. We describe the regular asymptotic procedure of averaging such equations and show that the averaged equations in the leading order already well describe the phenomenon of resonant phase locking in which the breather oscillations are strongly excited. We obtain necessary and sufficient conditions for the phase locking relating the rate of the perturbation frequency variation and its amplitude to the initial data of the breather.

Keywords: sine-Gordon equation, breather, phase locking, perturbation theory, asymptotic behavior, averaging.

DOI: 10.4213/tmf6092

 English version: Theoretical and Mathematical Physics, 2007, 152:2, 1173–1182

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