Normal Form for the Fractional Nonlinear Schrödinger Equation with Cubic Nonlinearity

• Fuzheng Ma ^[1] ; Xindong Xu ^[1]
  1. [1] Southeast University

     Southeast University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 3, 2023
• Idioma: inglés
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• Resumen

  • 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.