New solutions to the complex Ginzburg-Landau equations
Robert Conte (ENS Paris-Saclay), Micheline Musette (VUB Brussel), Ng, Tuen Wai (The University of Hong Kong), Wu Chengfa (Shenzhen university)
TL;DR
This paper presents three new exact solutions to the one-dimensional complex Ginzburg-Landau equation, including localized defects and bound states of dark solitons, enhancing understanding of pattern interactions in nonlinear systems.
Contribution
The paper introduces three analytically derived solutions for elementary patterns in the complex Ginzburg-Landau equation, previously only observed numerically.
Findings
Identification of a localized homoclinic defect in the quintic case.
Discovery of bound states of two quintic dark solitons.
Analytical solutions complement numerical observations.
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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