2020/09/27 by Derek Handwerk, Gerhard Dangelmayr, Handwerk, Derek +5 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #35B36 35Q56 35B35 35C07 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Pattern Formation and Solitons (nlin.PS) #Plant Reproductive Biology
paper · pdf · doi:10.48550/arxiv.2009.12945
openalex publication_date 2020/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.