KAM tori for defocusing modified KDV equation

Abstract In this paper, one-dimensional defocusing modified KDV equation: u t + u x x x − 6 u 2 u x = 0 with periodic boundary condition is considered. It is proved that the above equation admits a Cantor family of small amplitude, quasi-periodic solutions. The proof is based on an infinite dimensional KAM theorem and partial Birkhoff normal form.