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math.AP2024
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 mos…
math.AP2024
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…
math.AP2024★ 2 cited
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 term…