Communication: Restoring full size extensivity in internally contracted multireference coupled cluster theory J. Chem. Phys. 137, 131103 (2012) Analytical spatiotemporal soliton solutions to (3+1)-dimensional cubic-quintic nonlinear Schrödinger equation with distributed coefficients J. Math. Phys. 53, 103704 (2012) Time-domain determination of transmission in quantum nanostructures J. Appl. Phys. 112, 064325 (2012) The virial theorem for the smoothly and sharply, penetrably and impenetrably confined hydrogen atom J. Chem. Phys. 137, 114109 (2012) Communication: Phase space wavelets for solving Coulomb problemsIn this paper, we show that one dimension derivative nonlinear Schrödinger equation admits a whitney smooth family of small amplitude, real analytic quasiperiodic solutions with two Diophantine frequencies. The proof is based on a partial Birkhoff normal form reduction and an abstract infinite dimensional Kolmogorov-Arnold-Moser (KAM) theorem. C 2012 American Institute of Physics.Motivated by the classical Kolmogorov-Arnold-Moser (KAM) theory in finite dimensional Hamiltonian systems, to obtain quasi-periodic solutions, for an integer N > 1, one finds a parameter space O ⊂ R N and (symplectic) action-angle-normal coordinates I = (I 1 , . . . , θ = (θ 1 , . . . , θ N ), z = (z j ) j∈Z such that the Hamiltonian (1.3) can be transformed into a parametrized Hamiltonian normal formDenote d as the order of¯ j and δ as the order of the Hamiltonian vector field X P . We use d to measure the growth rate of the eigenvalue¯ j and δ to measure the unboundedness of X P . When δ ≤ 0, the vector field X P is called bounded perturbation, the existence of quasi-periodic solutions of such PDEs has been deeply and widely studied. There are plenty of papers dedicated to such these issues. See Refs. 2-6, 10, and 12 for example.When δ > 0, the vector field X P is called unbounded perturbation. In order to obtain the existence of quasi-periodic solutions for such PDEs, it is reasonable to assume δ ≤ d − 1, according to a well known example, which was referred in Klainerman 8 and Lax. 11 When 0 < δ < d − 1, the corresponding KAM theorem is due to Kuksin. 9 Kuksin's theorem is used to prove the existence of time quasi-periodic solutions of KdV equation subject to periodic boundary condition. See also For such unbounded perturbations, Bambusi-Graffi 1 gave another KAM theorem to prove that the time dependent linear Schrödinger equation has only pure point spectrum.When 0 < δ = d − 1, the nonlinearity of the PDE is the strongest. Liu-Yuan 17 gave a theorem, which generalized Kuksin's theorem from δ < d − 1 to δ ≤ d − 1. For the homological equations of variable coefficients(1.4) they developed some new estimate for the solution u covering not only the case δ < d − 1, but also the limit case δ = d − 1. Using the generalized Kuksin's theorem, Zhang-Gao-Yuan 19 established a KAM theorem for an infinite dimensional reversible system with unbounded perturbation and obtained many C ∞ (not real analytic) quasi-periodic solutions...