Hole solutions in the 1D complex Ginzburg-Landau equation

DOI10.1016/0167-2789(95)00070-KzbMath0884.35055arXivpatt-sol/9409002OpenAlexW3098810338MaRDI QIDQ5917641

Igor S. Aranson, Olaf Stiller, Lorenz Kramer, Stefan Popp

Publication date: 19 June 1995

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/patt-sol/9409002

zbMATH Keywords

hole-shock interactionmatching and perturbation methodsstructurally unstable solutionstraveling localized source solutions

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) NLS equations (nonlinear Schrödinger equations) (35Q55) Bifurcations in context of PDEs (35B32)

Related Items (8)

All meromorphic traveling waves of cubic and quintic complex Ginzburg-Landau equations ⋮ Standing waves of the complex Ginzburg-Landau equation ⋮ The cubic complex Ginzburg-Landau equation for a backward bifurcation ⋮ The diversity of steady state solutions of the complex Ginzburg-Landau equation ⋮ Dark soliton dynamics under the complex Ginzburg-Landau equation ⋮ Stability of nonlinear waves: pointwise estimates ⋮ All we know about hole solutions in the CGLE ⋮ Stability of oscillating hexagons in rotating convection

Cites Work

• Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations
• Spatiotemporal chaos in the one-dimensional complex Ginzburg-Landau equation
• Spatiotemporal intermittency regimes of the one-dimensional complex Ginzburg-Landau equation
• From dark solitons in the defocusing nonlinear Schrödinger to holes in the complex Ginzburg-Landau equation

This page was built for publication: Hole solutions in the 1D complex Ginzburg-Landau equation