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Teoreticheskaya i Matematicheskaya Fizika, 2003, Volume 137, Number 1, Pages 108–120
DOI: https://doi.org/10.4213/tmf249
(Mi tmf249)
 

This article is cited in 9 scientific papers (total in 9 papers)

The Influence of Modulational Instability on Energy Exchange in Coupled Sine-Gordon Equations

S. D. Griffithsa, R. Grimshawa, K. R. Khusnutdinovaab

a Loughborough University
b Institute of Mechanics, Ufa Centre of the Russian Academy of Sciences
References:
Abstract: We consider a two-component system of coupled sine-Gordon equations, particular solutions of which represent a continuum generalization of periodic energy exchange in a system of coupled pendulums. Weakly nonlinear solutions describing periodic energy exchange between waves traveling in the two components are governed, depending on the length scale of the amplitude variation, either by two nonlocally coupled nonlinear Schrцdinger equations, with different transport terms due to the group velocity, or by a model that is nondispersive to the leading order. Using both asymptotic analysis and numerical simulations, we show that the effects of dispersion significantly influence the structure of these solutions, causing modulational instability and the formation of localized structures but preserving the pattern of energy exchange between the components.
Keywords: coupled sine-Gordon equations, amplitude equations, linear waves, nonlinear waves, energy exchange in two-component systems, modulational instability.
English version:
Theoretical and Mathematical Physics, 2003, Volume 137, Issue 1, Pages 1448–1458
DOI: https://doi.org/10.1023/A:1026008907682
Bibliographic databases:
Language: Russian
Citation: S. D. Griffiths, R. Grimshaw, K. R. Khusnutdinova, “The Influence of Modulational Instability on Energy Exchange in Coupled Sine-Gordon Equations”, TMF, 137:1 (2003), 108–120; Theoret. and Math. Phys., 137:1 (2003), 1448–1458
Citation in format AMSBIB
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\by S.~D.~Griffiths, R.~Grimshaw, K.~R.~Khusnutdinova
\paper The Influence of Modulational Instability on Energy Exchange in Coupled Sine-Gordon Equations
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\pages 108--120
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\transl
\jour Theoret. and Math. Phys.
\yr 2003
\vol 137
\issue 1
\pages 1448--1458
\crossref{https://doi.org/10.1023/A:1026008907682}
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Linking options:
  • https://www.mathnet.ru/eng/tmf249
  • https://doi.org/10.4213/tmf249
  • https://www.mathnet.ru/eng/tmf/v137/i1/p108
  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
     
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