Submitting Campus
Daytona Beach
Department
Mathematics
Document Type
Article
Publication/Presentation Date
3-2007
Abstract/Description
In this paper we use a traveling wave reduction or a so{called spatial approxima- tion to comprehensively investigate the periodic solutions of the complex cubic{quintic Ginzburg{Landau equation. The primary tools used here are Hopf bifurcation theory and perturbation theory. Explicit results are obtained for the post{bifurcation periodic orbits and their stability. Generalized and degenerate Hopf bifurcations are also brie y considered to track the emergence of global structure such as homoclinic orbits.
Publication Title
Mathematics and Computers in Simulation
DOI
https://doi.org/10.1016/j.matcom.2006.10.022
Publisher
Elsevier
Scholarly Commons Citation
Mnacas, S., & Choudhury, S. R. (2007). The Complex Cubi-Quintic Ginzburg-Landau Equation: Hopf Bifurcations Yielding Traveling Waves. Mathematics and Computers in Simulation, 74(4/5). https://doi.org/10.1016/j.matcom.2006.10.022
Additional Information
Dr. Mancas was not affiliated with Embry-Riddle Aeronautical University at the time this articles was published.