Bounds on the growth of high discrete Sobolev norms for the cubic discrete nonlinear Schrödinger equations on $h\mathbb{Z}$

Joackim Bernier (1)

1 MINGUS - Multi-scale numerical geometric schemes

We consider the discrete nonlinear Schrödinger equations on a one dimensional lattice of mesh h, with a cubic focusing or defocusing nonlinearity. We prove a polynomial bound on the growth of the discrete Sobolev norms, uniformly with respect to the stepsize of the grid. This bound is based on a construction of higher modified energies.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Joackim Bernier. Bounds on the growth of high discrete Sobolev norms for the cubic discrete nonlinear Schrödinger equations on $h\mathbb{Z}$. Discrete and Continuous Dynamical Systems - Series A, 2019, 39 (6), pp.3179-3195. ⟨10.3934/dcds.2019131⟩. ⟨hal-01785953v2⟩