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New solutions to the complex Ginzburg-Landau equations (2208.14945v1)

Published 31 Aug 2022 in nlin.PS, cond-mat.other, math-ph, and math.MP

Abstract: The various r\'egimes 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, sinks. We provide here three exact such patterns observed in numerical calculations but never found analytically. One is a quintic case localized homoclinic defect, observed by Popp et alii, the two others are bound states of two quintic dark solitons, observed by Afanasyev et alii.

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