Stabilization of pulses by competing stability mechanisms.

Abstract
The (cubic) Ginzburg-Landau equation has various
unstable solitary pulse solutions, which have, however,
been observed in systems with two competing instability
mechanisms. In such systems, the Ginzburg-
Landau equation is coupled to a diffusion equation. In
previous work, it has been shown by an Evans function
approach that the effect of the slow diffusion can
indeed stabilize a pulse when the diffusive mode is
(weakly) damped, and when higher-order nonlinearities
are taken into account. In the current work the
more natural case where the diffusion equation has a
neutrally stable mode at kc = 0 is studied by means
of asymptotic expansions. The neutrally stable mode
introduces pulses that decay algebraically rather than
exponentially, which is essential for the Evans function
approach.

Key words
Ginzburg-Landau, asymptotic expansions, pulse solution,
stabilization.