1999/09/15 by Piero de Mottoni, P. de Mottoni, de Mottoni, Piero +2
Mathematics · Physics and Astronomy · #34C37 #35B25 #35B32 #35B35 #35B40 #35K57 #35Q99 #Analysis of PDEs (math.AP) #FOS: Mathematics #Laser-Plasma Interactions and Diagnostics #Magnetic confinement fusion research #Quantum chaos and dynamical systems #math.AP #msc:34C37 #msc:35B25 #msc:35B32 #msc:35B35 #msc:35B40 #msc:35K57 #msc:35Q99
paper · pdf · doi:10.48550/arxiv.math/9909083
AMS-LaTeX; 54 pages, 6 figures. Improves a preprint which was circulated in 1993, but never reached the desirable quality of exposition. Includes new results
arxiv created 1999/09/15 · openalex publication_date 1999/09/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.