Claudio Muñoz

Nonlinear Stability of MKdV Breathers

Breather solutions of the modified Korteweg-de Vries equation are shown to be globally stable in a naturalH2 topology. Our proof introduces a new Lyapunov functional, at the H2 level, which allows to describe the dynamics of small perturbations, including oscillations induced by the periodicity of the solution, as well as a direct control of the corresponding instability modes. In particular, degenerate directions are controlled using low-regularity conservation laws.

Kink dynamics in the ⁴ model: Asymptotic stability for odd perturbations in the energy space

We consider a classical equation known as the

Singular limits for the bi-Laplacian operator with exponential nonlinearity in R4

\phi^4

The Gardner equation and the ²-stability of the -soliton solution of the Korteweg-de Vries equation

model in one space dimension. The kink, defined by

Nonexistence of small, odd breathers for a class of nonlinear wave equations

H(x)=\tanh(x/{\sqrt{2}})

On the soliton dynamics under a slowly varying medium for generalized KdV equations

, is an explicit stationary solution of this model. From a result of Henry, Perez and Wreszinski it is known that the kink is orbitally stable with respect to small perturbations of the initial data in the energy space. In this paper we show asymptotic stability of the kink for odd perturbations in the energy space. The proof is based on Virial-type estimates partly inspired from previous works of Martel and Merle on asymptotic stability of solitons for the generalized Korteweg-de Vries equations. However, this approach has to be adapted to additional difficulties, pointed out by Soffer and Weinstein in the case of general Klein-Gordon equations with potential: the interactions of the so-called internal oscillation mode with the radiation, and the different rates of decay of these two components of the solution in large time.

Asymptotic Stability of High-dimensional Zakharov-Kuznetsov Solitons

Let

On the nonlinear stability of mKdV breathers

\Omega

On the solitary wave dynamics, under slowly varying medium, for nonlinear Schrödinger equations

be a bounded smooth domain in

Occupational exposure to polycyclic aromatic hydrocarbons: A cross-sectional study in bars and restaurants in Santiago, Chile

\mathbb{R}^{4}