  It is possible to choose the parameters of a real quintic Ginzburg-Landau
equation so that it possesses localized pulse-like solutions; Thual and Fauve
have observed numerically that these pulses are stabilized by perturbations
destroying the gradient structure of the real equation. For parameters such
that the real part of the equations possesses pulses with a large shelf, we
prove the existence of pulses by validated asymptotics, we find the expansion
of the small eigenvalues of the operator and of their corresponding
eigenvectors, and we give a sufficient condition for stabilization. This
condition is generalized to any small non-gradient quintic perturbation of
Ginzburg-Landau.
