3 papers
math.AP2025
Transverse asymptotic stability of line solitary waves for the Ionic Euler-Poisson system
Frédéric Rousset, Changzhen Sun
We prove the linear and nonlinear asymptotic stability of small amplitude one-dimensional solitary waves submitted to small localized irrotational perturbations in the three dimens…
math.AP2024
Transverse linear stability of one-dimensional solitary gravity water waves
Frédéric Rousset, Changzhen Sun
In this paper, we establish the transverse linear asymptotic stability of one-dimensional small-amplitude solitary waves of the gravity water-waves system. More precisely, we show…
math.AP2009
A simple criterion of transverse linear instability for solitary waves
F. Rousset, N. Tzvetkov
We prove an abstract instability result for an eigenvalue problem with parameter. We apply this criterion to show the transverse linear instability of solitary waves on various exa…