Resumen de Normal Form for the Fractional Nonlinear Schrödinger Equation with Cubic Nonlinearity

Fuzheng Ma, Xindong Xu

• We study the Birkhoff normal form for the cubic Fractional NLS iut − (|∂x | + σ ) 1 2 u + |u| 2u = 0, x ∈ T, t ∈ R.

  It is proved that there exists some interval I ⊂ [0, 1], such that for any σ ∈ I, the equation above admits a family of small-amplitude, linearly stable quasi-periodic solutions.