The Complex Cubic-Quintic Ginzburg-Landau Equation: Hopf Bifurcations Yielding Traveling Waves

S.C. Mancas; S. Roy Choudhury; Stefani Mancas

doi:10.1016/j.matcom.2006.10.022

The Complex Cubic-Quintic Ginzburg-Landau Equation: Hopf Bifurcations Yielding Traveling Waves

S.C. Mancas, S. Roy Choudhury, Stefani Mancas

Embry-Riddle Aeronautical University

Research output: Contribution to journal › Article › peer-review

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.

Original language	American English
Journal	Mathematics and Computers in Simulation
Volume	74
DOIs	https://doi.org/10.1016/j.matcom.2006.10.022
State	Published - Mar 30 2007

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Mathematics

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title = "The Complex Cubic-Quintic Ginzburg-Landau Equation: Hopf Bifurcations Yielding Traveling Waves",

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. ",

author = "S.C. Mancas and Choudhury, {S. Roy} and Stefani Mancas",

note = "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.",

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AU - Choudhury, S. Roy

AU - Mancas, Stefani

N1 - 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.

PY - 2007/3/30

Y1 - 2007/3/30

N2 - 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.

AB - 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.

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DO - 10.1016/j.matcom.2006.10.022

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VL - 74

JO - Mathematics and Computers in Simulation

JF - Mathematics and Computers in Simulation

ER -

The Complex Cubic-Quintic Ginzburg-Landau Equation: Hopf Bifurcations Yielding Traveling Waves

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