The complex cubic–quintic Ginzburg–Landau equation: Hopf bifurcations yielding traveling waves

Stefan C. Mancas and S.Roy Choudhury

Mathematics and Computers in Simulation (MATCOM), 2007, vol. 74, issue 4, 281-291

Abstract: In this paper we use a traveling wave reduction or a so-called spatial approximation 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 briefly considered to track the emergence of global structure such as homoclinic orbits.

Keywords: Periodic; Wavetrains; Hopf bifurcations; CGLE (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:74:y:2007:i:4:p:281-291

DOI: 10.1016/j.matcom.2006.10.022

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