- 95-140 Eckmann J.-P., Gallay Th., Wayne C.E.
- Phase Slips and the Eckhaus Instability
(214K, Postscript)
Mar 8, 95
-
Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers
-
Abstract. We consider the Ginzburg-Landau equation,
$
\partial_t u= \partial_x^2 u + u - u|u|^2
$,
with complex amplitude $u(x,t)$.
We first analyze the phenomenon of
phase slips as a consequence of the {\it local} shape of $u$. We next prove a
{\it global} theorem about evolution from an Eckhaus unstable state,
all the way to the limiting stable finite state, for periodic perturbations of
Eckhaus unstable periodic initial data.
Equipped with these results, we proceed to prove the
corresponding phenomena for the fourth order Swift-Hohenberg equation,
of which the Ginzburg-Landau equation is the amplitude approximation.
This sheds light on how one should deal with
local and global aspects of phase slips for this and
many other similar systems.
- Files:
95-140.ps