# BIRKHOFF NORMAL FORM FOR ABCD BOUSSINESQ SYSTEM ON THE CIRCLE

Nom de l'orateur
Nguyen Trung
Etablissement de l'orateur
LMJL
Date et heure de l'exposé
Lieu de l'exposé
salle zoom

## Séminaire d'analyse

In this paper, we prove a Birkhoff normal form result for abcd Boussinesq system on the circle with $b = d > 0; a; c < 0$. The result is based on the fact that the nonlinear term has a so-called tame modulus and the frequencies satisfy nonresonant condition.
As a consequence of the Birkhoff normal form, we have that any small amplitude solution remains close to a torus for a long time.