Phase-Diffusion Equations for the Anisotropic Complex Ginzburg-Landau Equation
Pattern Formation and Solitons
2020-09-29 v1 Analysis of PDEs
Dynamical Systems
Abstract
The anisotropic complex Ginzburg-Landau equation (ACGLE) describes slow modulations of patterns in anisotropic spatially extended systems near oscillatory (Hopf) instabilities with zero wavenumbers. Traveling wave solutions to the ACGLE become unstable near Benjamin-Feir-Newell instabilities. We determine two instability conditions in parameter space and study codimension-one (-two) bifurcations that occur if one (two) of the conditions is (are) met. We derive anisotropic Kuramoto-Sivashinsky-type equations that govern the phase of the complex solutions to the ACGLE and generate solutions to the ACGLE from solutions of the phase equations.
Cite
@article{arxiv.2009.12945,
title = {Phase-Diffusion Equations for the Anisotropic Complex Ginzburg-Landau Equation},
author = {Derek Handwerk and Gerhard Dangelmayr and Iuliana Oprea and Patrick D. Shipman},
journal= {arXiv preprint arXiv:2009.12945},
year = {2020}
}
Comments
15 pages, 8 figures