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

This paper is concerned with a one dimensional derivative nonlinear Schrodinger equation with quasi-periodic forcing under periodic boundary conditions iu t + u xx + ig(fit)(f(|u|²)u)x = 0, x ∊ T := R/2πZ, where g(βt) is real analytic and quasi-periodic on t with frequency vector β = (β 1 ,β 2 ,..., β m ). f is real analytic in some neighborhood of the origin in C, f (0) = 0 and f'(0) ≠ 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. [ABSTRACT FROM AUTHOR]

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