On the quasilinear Schrödinger equations on tori

Abstract We improve the result by Feola and Iandoli (J Math Pures Appl 157: 243–281, 2022), showing that quasilinear Hamiltonian Schrödinger type equations are well posed on Hˢ ({ {T}}ᵈ) H s (T d) if s>d/2+3 s > d / 2 + 3. We exploit the sharp paradifferential calculus on { {T}}ᵈ T d developed by Berti et al. (J Dyn Differ Equ 33 (3): 1475–1513, 2021).