##
Derivation of the time-dependent Ginzburg-Landau
equation on the line

* J. Nonlin. Sci.* **8** (1998) 1-15

** Ian Melbourne **

** Abstract **

We give a rigorous derivation of the time-dependent
one-dimensional Ginzburg-Landau equation.

As in the work of Iooss, Mielke and Demay (who derived the steady
Ginzburg-Landau equation) our derivation leads to
a pseudodifferential complex amplitude equation with nonlocal terms of
all orders that yields the
cubic order Ginzburg-Landau equation when truncated. The truncation
step itself is not justified by our methods.

Furthermore, we prove that the nontruncated Ginzburg-Landau equation
has a normal form **SO**(2) symmetry to arbitrarily high order.
The normal form symmetry forces the equation to be odd with constant
coefficients. This structure is broken in the tail.

**Postscript file**
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