Title: Periodic fourth-order cubic NLS: Local well-posedness and Non-squeezing property,
Abstract: In this paper, we consider the cubic fourth-order nonlinear Schrödinger
equation (4NLS) under the periodic boundary condition. We prove two results.
One is the local well-posedness in $H^s$ with $-1/3 \le s < 0$ for the Cauchy
problem of the Wick ordered 4NLS. The other one is the non-squeezing property
for the flow map of 4NLS in the symplectic phase space $L^2(\mathbb{T})$. To
prove the former we used the ideas introduced in [Takaoka and Tsutsumi 2004]
and [Nakanish et al 2010], and to prove the latter we used the ideas in
[Colliander et al 2005].