Invariant tori for a derivative nonlinear Schrodinger equation with quasi-periodic forcing

This paper is concerned with a one dimensional derivative nonlinear Schrdinger equation with quasi-periodic forcing under periodic boundary conditions iu(t) + u(xx) + ig(beta t)(f (|u|(2))u)(x) = 0, x is an element of T := R/2 pi Z, where g(beta t) is real analytic and quasi-periodic on t with frequency vector beta = (beta(1), beta(2),...,beta(m)). f is real analytic in some neighborhood of the origin in C, f (0) = 0 and f '(0) not equal 0. We show that the above equation admits Cantor families of smooth quasi-periodic solutions of small amplitude. The proof is based on an abstract infinite dimensional Kolmogorov-Arnold-Moser theorem for unbounded perturbation vector fields and partial Birkhoff normal form. (C) 2015 AIP Publishing LLC.