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Teoreticheskaya i Matematicheskaya Fizika, 2007, Volume 152, Number 2, Pages 356–367
DOI: https://doi.org/10.4213/tmf6092 (Mi tmf6092) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Breather resonant phase locking by an external perturbation

E. M. Maslova, L. A. Kalyakinb, A. G. Shagalovc

a 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
Full-text PDF (603 kB) Citations (9)
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DOI: https://doi.org/10.4213/tmf6092
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.
English version:
Theoretical and Mathematical Physics, 2007, Volume 152, Issue 2, Pages 1173–1182
DOI: https://doi.org/10.1007/s11232-007-0100-6
Bibliographic databases:
Language: Russian
Citation: E. M. Maslov, L. A. Kalyakin, A. G. Shagalov, “Breather resonant phase locking by an external perturbation”, TMF, 152:2 (2007), 356–367; Theoret. and Math. Phys., 152:2 (2007), 1173–1182
Citation in format AMSBIB
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\paper Breather resonant phase locking by an~external perturbation
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\pages 356--367
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  • https://doi.org/10.4213/tmf6092
  • https://www.mathnet.ru/eng/tmf/v152/i2/p356
    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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