ANALYTICITY OF GINZBURG-LANDAU MODES

Ginzburg-Landau formalism applies for dissipative systems defined on c ylindrical domains which are close to the threshold ol instability and for which the unstable Fourier modes belong to non-zero wave numbers. In these situations the real part of the curve of critical eigenvalue s as function drawn over the wave numbers k is positive of height Omic ron(epsilon(2)) and of width Omicron(epsilon). Here it is shown that t he set of solutions which can be described by the Ginzburg-Landau form alism is attractive. To do this we demonstrate that in Fourier space p eaks appear at integer multiples of the critical wave number k(c). The se peaks called Ginzburg-Landau modes concentrate in time like e(-\k-m kc\root t) for 0 less than or equal to t less than or equal to Omicron (1/epsilon(2)) and m is an element of Z. The inverse Fourier transform of such a Ginzburg-Landau mode is an analytic Function in a strip of width root t. This result extends a former work of W. Eckhaus. (C) 199 5 Academic Press, Inc.