Existence and stability of traveling waves for discrete nonlinear Schroedinger equations over long times

Joackim Bernier (1) , Erwan Faou (1)

1 MINGUS - Multi-scale numerical geometric schemes

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, near the continuous limit.We construct a family of solutions close to the continuous traveling waves and prove their stability over long times. Applying a modulation method, we also show that we can describe the dynamics near these discrete traveling waves over long times.

Mots clés: Discrete nonlinear schroedinger equation; solitary waves

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

Joackim Bernier, Erwan Faou. Existence and stability of traveling waves for discrete nonlinear Schroedinger equations over long times. SIAM Journal on Mathematical Analysis, 2019, 51 (3), pp.1607-1656. ⟨10.1137/18M1186484⟩. ⟨hal-01788398⟩