On the quasilinear Schrödinger equations on tori

We improve the result by Feola and Iandoli [J. de Math. Pures et App., 157:243-281, 2022], showing that quasilinear Hamiltonian Schrödinger type equations are well posed on $H^s({\mathbb{T}}^d)$ if $s>d\mathrm{/}2+3$. We exploit the sharp paradifferential calculus on ${\mathbb{T}}^d$ introduced by Berti, Maspero and Murgante [J. Dynam. and Differential Equations, 33 (3): 1475-1513, 2021].