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

    Authors

    S. R. Choudhury

    Comments

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    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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