On the quasilinear Schrödinger equations on tori

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(Tᵈ) H s ( T d ) if $$s>d/2+3$$ s > d / 2 + 3 . We exploit the sharp paradifferential calculus on Tᵈ T d developed by Berti et al. (J Dyn Differ Equ 33(3):1475–1513, 2021).