Title

Modulated amplitude waves in the cubic-quintic Ginzburg-Landau equation

Authors

Authors

S. R. Choudhury

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

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

WOS:000230029600004

ISSN

0378-4754

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