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Journal Articles Physical Review E Year : 2022

New solutions to the complex Ginzburg-Landau equations

Abstract

The various regimes observed in the one-dimensional complex Ginzburg-Landau equation result from the interaction of a very small number of elementary patterns such as pulses, fronts, shocks, holes, and sinks. Here we provide three exact such patterns observed in numerical calculations but never found analytically. One is a quintic case localized homoclinic defect, observed by Popp et al. [S. Popp et al., Phys. Rev. Lett. 70, 3880 (1993)], and the two others are bound states of two quintic dark solitons, observed by Afanasyev et al. [V. V. Afanasyev et al., Phys. Rev. E 57, 1088 (1998)].
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Dates and versions

hal-04547537 , version 1 (15-05-2024)

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Robert Conte, Micheline Musette, Tuen Wai Ng, Chengfa Wu. New solutions to the complex Ginzburg-Landau equations. Physical Review E , 2022, 106 (4), pp.L042201. ⟨10.1103/PhysRevE.106.L042201⟩. ⟨hal-04547537⟩
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