New solutions to the complex Ginzburg-Landau equations
Pattern Formation and Solitons
2022-10-19 v1 Other Condensed Matter
Mathematical Physics
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.
Keywords
Cite
@article{arxiv.2208.14945,
title = {New solutions to the complex Ginzburg-Landau equations},
author = {Robert Conte and Micheline Musette and Ng Tuen Wai and Wu Chengfa},
journal= {arXiv preprint arXiv:2208.14945},
year = {2022}
}
Comments
7 pages, 3 figures, to appear, Physical Review E