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.
Cite this article
R. Feola, F. Iandoli, Local well-posedness for quasi-linear NLS with large Cauchy data on the circle. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 1, pp. 119–164DOI 10.1016/J.ANIHPC.2018.04.003