Title
Modulated amplitude waves in the cubic-quintic Ginzburg-Landau equation
Abbreviated Journal Title
Math. Comput. Simul.
Keywords
coherent structures; modulated amplitude waves; cubic-quintic; Ginzburg-Landau equation; ECKHAUS INSTABILITY; PULSES; STABILITY; CHAOS; Computer Science, Interdisciplinary Applications; Computer Science, ; Software Engineering; Mathematics, Applied
Abstract
In this paper, we begin to develop a theoretical framework for analyzing the strongly amplitude modulated numerical pulse solutions recently observed in the complex Ginzburg-Landau Equation, which is a canonical model for dissipative, weakly nonlinear systems. As such, the article also reviews background concepts of relevance to coherent structures in general dissipative systems (in regimes where such structures are stable and dominate the dynamics). This framework allows a comprehensive analysis of various bifurcations leading to transitions from one type of coherent structure to another as the system parameters are varied. It will also form a basis for future theoretical analysis of the great diversity of numerically-observed solutions, including even the spatially coherent structures with temporally quasiperiodic or chaotic envelopes observed in recent simulations. (c) 2004 IMACS. Published by Elsevier B.V. All rights reserved.
Journal Title
Mathematics and Computers in Simulation
Volume
69
Issue/Number
3-4
Publication Date
1-1-2005
Document Type
Article; Proceedings Paper
Language
English
First Page
243
Last Page
256
WOS Identifier
ISSN
0378-4754
Recommended Citation
"Modulated amplitude waves in the cubic-quintic Ginzburg-Landau equation" (2005). Faculty Bibliography 2000s. 5069.
https://stars.library.ucf.edu/facultybib2000/5069
Comments
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