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Updated: Aug 20, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
New solutions to the complex Ginzburg-Landau equations
Robert Conte1, Micheline Musette2, Tuen Wai Ng3
1Université Paris-Saclay, ENS Paris-Saclay, CNRS, Centre Borelli, F-91190 Gif-sur-Yvette, France and Department of Mathematics, The University of Hong Kong, Pokfulam, Hong Kong.
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)10.1103/PhysRevLett.70.3880], 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)10.1103/PhysRevE.57.1088].
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