Exact Solutions of the One-Dimensional Quintic Complex Ginzburg-Landau Equation

Details Exact Solutions of the One-Dimensional Quintic Complex Ginzburg-Landau Equation Exact Solutions of the One-Dimensional Quintic Complex Ginzburg-Landau Equation

1993-10-22

arxiv.org/abs/patt-sol/9310004v1

Nonlinear Sciences

Pattern Formation and Solitons

24 pages, regular LaTeX, no figures

Scientific paper

10.1016/0167-2789(94)90102-3

Exact solitary wave solutions of the one-dimensional quintic complex Ginzburg-Landau equation are obtained using a method derived from the Painlev\'e test for integrability. These solutions are expressed in terms of hyperbolic functions, and include the pulses and fronts found by van Saarloos and Hohenberg. We also find previously unknown sources and sinks. The emphasis is put on the systematic character of the method which breaks away from approaches involving somewhat ad hoc Ans\"atze.

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