We prove local in time well-posedness for a large class of quasilinear Hamiltonian, or parity preserving, Schrödinger equations on the circle. After a paralinearization of the equation, we perform several paradifferential changes of coordinates in order to transform the system into a paradifferential one with symbols which, at the positive order, are constant and purely imaginary. This allows to obtain a priori energy estimates on the Sobolev norms of the solutions.

VL - 36 UR - http://www.sciencedirect.com/science/article/pii/S0294144918300428 ER -