We consider the asymptotic behavior of small global-in-time solutions to a 1D Klein–Gordon
equation with a spatially localized, variable coefficient quadratic nonlinearity and a non …

We establish the asymptotic stability of the sine-Gordon kink under odd perturbations that
are sufficiently small in a weighted Sobolev norm. Our approach is perturbative and does not …

We initiate the study of the asymptotic behavior of small solutions to one-dimensional Klein-
Gordon equations with variable coefficient quadratic nonlinearities. The main discovery in …

We consider the codimension one asymptotic stability problem for the soliton of the focusing
cubic Klein-Gordon equation on the line under even perturbations. The main obstruction to …

We establish the full asymptotic stability of solitary waves for the focusing cubic Schr\"
odinger equation on the line under small even perturbations in weighted Sobolev norms …

We obtain sharp decay estimates and asymptotics for small solutions to the one-dimensional
Klein--Gordon equation with constant coefficient cubic and spatially localized, variable …

Let u be a solution to a quasi-linear Klein-Gordon equation in one-space dimension, $\Box
u+ u= P (u, $\partial $\_t u, $\partial $\_x u; $\partial $\_t $\partial $\_x u, $\partial $^ 2\_x u) …

We consider the global evolution problem for Einstein's field equations in the near-
Minkowski regime and study the long-time dynamics of a massive scalar field evolving under …

We establish the full asymptotic stability of the sine-Gordon kink outside symmetry under
small perturbations in weighted Sobolev norms. Our proof consists of a space-time …

We study the initial value problem for the Einstein–Klein–Gordon system and establish the
global nonlinear stability of massive matter in the near-Minkowski regime when the initial …