Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations. (English) Zbl 0763.35088

van Saarloos, Wim; Hohenberg, P. C.

Physica D 56, No. 4, 303-367 (1992).

This paper summarizes and extends recent work on “coherent structures” in the one-dimensional complex Ginzburg-Landau equation and its generalization, for which a comprehensive analysis of coherent structure solutions, i.e. fronts, pulses, sources and sinks is given.
Besides studying the multiplicity of coherent structures, the authors also discuss a number of exact results about symmetries, conservation laws, and exact coherent structure solutions. Furthermore, the authors formulate their basic selection conjectures regarding front pulse competition, which generalize the “marginal stability” and “pinch- point” approaches of earlier authors. Moreover, these conjectures are tested and verified by numerical calculation and analytical perturbation theory.

Reviewer: Guo Boling (Beijing)

MSC:

35Q55	NLS equations (nonlinear Schrödinger equations)
37C75	Stability theory for smooth dynamical systems
34D30	Structural stability and analogous concepts of solutions to ordinary differential equations
60G44	Martingales with continuous parameter

Keywords:

coherent structures; multiplicity; symmetries; conservation laws; selection conjectures

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