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Ginzburg-Landau system of complex modulation equations for distributed nonlinear dissipative transmission lines

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Nonlinear Oscillations

Abstract

The envelope modulation of a monoinductance transmission line is reduced to generalized coupled Ginzburg-Landau equations, from which a single cubic-quintic Ginzburg-Landau equation containing derivatives with respect to the space variable in the cubic terms is deduced. We investigate the modulational instability of the space wave solutions of both the system and the single equation. For the generalized coupled Ginzburg-Landau system, we consider only the zero wave numbers of the perturbations whose modulational instability conditions depend only on the coefficients of the system and the wave numbers of the carriers. In this case, a modulational instability criterion is established, which depends on both the perturbation wave numbers and the carrier. We also study the coherent structures of the generalized coupled Ginzburg-Landau system and present some numerical results.

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Authors and Affiliations

  1. University of Dschang, Dschang, Cameroon

    E. Kengne

  2. University of Ottawa, Ottawa, Canada

    E. Kengne & R. Vaillancourt

Authors
  1. E. Kengne
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  2. R. Vaillancourt
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Published in Neliniini Kolyvannya, Vol. 9, No. 4, pp. 451–489, October–December, 2006.

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Kengne, E., Vaillancourt, R. Ginzburg-Landau system of complex modulation equations for distributed nonlinear dissipative transmission lines. Nonlinear Oscill 9, 438–477 (2006). https://doi.org/10.1007/s11072-006-0055-9

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  • DOI: https://doi.org/10.1007/s11072-006-0055-9

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