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 Hs(T) with −1/3≤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 L2(T). To prove the former we used the ideas introduced in  and , and to prove the latter we used the ideas in .
|Number of pages||38|
|Journal||Journal of Mathematical Analysis and Applications|
|State||Published - 15 May 2018|
- Fourth-order NLS
- Local well-posedness
- Non-squeezing property
- Wick ordered NLS