The ThualFauve pulse: skew stabilization
Abstract
It is possible to choose the parameters of a real quintic GinzburgLandau equation so that it possesses localized pulselike 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 nongradient quintic perturbation of GinzburgLandau.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 September 1999
 arXiv:
 arXiv:math/9909083
 Bibcode:
 1999math......9083D
 Keywords:

 Mathematics  Analysis of PDEs;
 35B25;
 35B35;
 35Q99;
 34C37;
 35K57;
 35B32;
 35B40
 EPrint:
 AMSLaTeX