37 citations · 110 across the 23 of their papers we have counts for
4 papers · 1 filter
Rational normal forms and stability of small solutions to nonlinear Schrödinger equations
Joackim Bernier, Erwan Faou, Benoit Grebert
We consider general classes of nonlinear Schrödinger equations on the circle with nontrivial cubic part and without external parameters. We construct a new type of normal forms, na…
Smoothing Properties of Fractional Ornstein-Uhlenbeck Semigroups and Null-Controllability
Paul Alphonse, Joackim Bernier
We study fractional hypoelliptic Ornstein-Uhlenbeck operators acting on satisfying the Kalman rank condition. We prove that the semigroups generated by these op…
Existence and stability of traveling waves for discrete nonlinear Schroedinger equations over long times
Joackim Bernier, Erwan Faou
We consider the problem of existence and stability of solitary traveling waves for the one dimensional discrete non linear Schroedinger equation (DNLS) with cubic nonlinearity, nea…
Bounds on the growth of high discrete Sobolev norms for the cubic discrete nonlinear Schr{ö}dinger equations on
Joackim Bernier
We consider the discrete nonlinear Schr{ö}dinger equations on a one dimensional lattice of mesh h, with a cubic focusing or defocusing nonlinearity. We prove a polynomial bound on…