J Austral Math Soc Ser B 36 pp313--324, 1995.

On the Cauchy problem for the 1+2 complex Ginzburg-Landau equation

Charles Bu

(Received 31 August 1992; revised 1 May 1993)

Abstract

We present analytical methods to investigate the Cauchy problem for the complex Ginzburg-Landau equation ut = (n + ia)D u - (k + ib) |u|2q u + g u in 2 spatial dimensions (here all parameters are real). We first obtain the local existence for n > 0, k ³ 0. Global existence is established in the critical case q = 1. In addition, we prove the global existence when q = 2 if (1) |b| £ (Ö5 / 2)k or (2) ab > 0.

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Author

Charles Bu
Department of Mathematics, Wellesley College, Wellesley, Massachusetts 02181, U.S.A.