7 papers
Arbitrary high order splitting methods for linear Schr{ö}dinger equations with non-trivial compatibility conditions
Joackim Bernier, Ramona Häberli, Gilles Vilmart
Splitting methods are a natural choice for the numerical time integration of partial differential equations, and arbitrary high order splitting schemes exist for Schr{ö}dinger equ…
Almost global existence for Hamiltonian PDEs on compact manifolds
Dario Bambusi, Joackim Bernier, Benoît Grébert +1
We prove an abstract result of almost global existence of small solutions to semi-linear Hamiltonian partial differential equations satisfying very weak non resonance conditions an…
Long time stability for cubic nonlinear Schrödinger equations on non-rectangular flat tori
Joackim Bernier, Nicolas Camps
We consider nonlinear Schrödinger equations on flat tori satisfying a simple and explicit Diophantine non-degeneracy condition. Provided that the nonlinearity contains a cubic ter…
On almost periodic solutions to NLS without external parameters
Joackim Bernier, Benoît Grébert
In this note, we present a result established in [BGR24] where we prove that nonlinear Schrodinger equations on the circle, without external parameters, admit plenty of infinite di…
Almost conservation of the harmonic actions for fully discretized nonlinear Klein--Gordon equations at low regularity
Charbella Abou Khalil, Joackim Bernier
Close to the origin, the nonlinear Klein--Gordon equations on the circle are nearly integrable Hamiltonian systems which have infinitely many almost conserved quantities called har…
Infinite dimensional invariant tori for nonlinear Schrödinger equations
Joackim Bernier, Benoit Grébert, Tristan Robert
We prove that nonlinear Schrödinger equations on the circle, without external parameters, admits plenty of almost periodic solutions. Indeed, we prove that arbitrarily close to mo…