Multi-order exact solutions of the complex Ginzburg-Landau equation

The multi-order exact solutions of the one-dimensional complex Ginzburg-Lan dau equation are obtained by the use of the wave packet theory. In these so lutions, the zeroth-order exact solution is a plane wave; the first-order e xact solutions are shock waves between the amplitude and the shift of phase , spiral waves between the shift of phase and distance or between the shift of phase and the amplitude; the second-order exact solutions are two perio dic waves with certain conditions and their limits - the shock waves and so litary waves can also be found. (C) 2000 Elsevier Science B.V. All rights r eserved.