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Linearized dynamic stability for vortices of Ginzburg-Landau evolutions
José M. Palacios, Fabio Pusateri
We consider the problem of dynamical stability for the -vortex of the Ginzburg-Landau model. Vortices are one of the main examples of topological solitons, and their dynamic sta…
Local well-posedness for the gKdV equation on the background of a bounded function
José Manuel Palacios
We prove the local well-posedness for the generalized Korteweg-de Vries equation in , , under general assumptions on the nonlinearity , on the backgro…
Orbital stability and instability of periodic wave solutions for -models
Gong Chen, José M. Palacios
In this work we study the orbital stability/instability in the energy space of a specific family of periodic wave solutions of the general -model for all .…
Orbital stability and instability of periodic wave solutions for the -model
José Manuel Palacios
In this work we find explicit periodic wave solutions for the classical -model, and study their corresponding orbital stability/instability in the energy space. In particular,…
Orbital and asymptotic stability of a train of peakons for the Novikov equation
José Manuel Palacios
The Novikov equation is an integrable Camassa-Holm type equation with cubic nonlinearity. One of the most important features of this equation is the existence of peakon and multi-p…
Asymptotic stability of peakons for the Novikov equation
José Manuel Palacios
The Novikov equation is a Camassa-Holm type equation with cubic nonlinearity. This paper aims to prove the asymptotic stability of peakons solutions under -perturb…