Ginzburg-Landau system of complex modulation equations for a distributed nonlinear-dispersive transmission line
The envelope modulation of a monoinductance transmission line is reduced to generalized coupled Ginzburg – Landau equations from which is deduced a single cubic-quintic Ginzburg – Landau equation containing derivatives with respect to the spatial variable in the cubic terms. We investigate the modul...
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| Date: | 2006 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2006
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| Series: | Нелінійні коливання |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/178173 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Ginzburg-Landau system of complex modulation equations for a distributed nonlinear-dispersive transmission line / E. Kengne, R. Vaillancourt // Нелінійні коливання. — 2006. — Т. 9, № 4. — С. 451-489. — Бібліогр.: 31 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | The envelope modulation of a monoinductance transmission line is reduced to generalized coupled Ginzburg – Landau equations from which is deduced a single cubic-quintic Ginzburg – Landau equation containing derivatives with respect to the spatial variable in the cubic terms. We investigate the modulational
instability of the spatial wave solutions of both the system and the single equation. For the generalized
coupled Ginzburg – Landau system we consider only the zero wavenumbers of the perturbations whose
modulational instability conditions depend only on the system’s coefficients and the wavenumbers of
the carriers. In this case, a modulational instability criterion is established which depends both on the
perturbation wavenumbers and the carrier. We also study the coherent structures of the generalized coupled
Ginzburg – Landau system and present some numerical studies. |
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