Periodic fourth-order cubic NLS: Local well-posedness and Non-squeezing property

Chulkwang Kwak

Periodic fourth-order cubic NLS: Local well-posedness and Non-squeezing property

Analysis of PDEs 2018-01-25 v2

Authors: Chulkwang Kwak

Abstract

In this paper, we consider the cubic fourth-order nonlinear Schr\"odinger 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].

Keywords

fourth-order nonlinear Schrödinger equation periodic boundary condition local well-posedness non-squeezing property symplectic phase space

Cite

@article{arxiv.1708.00127,
  title  = {Periodic fourth-order cubic NLS: Local well-posedness and Non-squeezing property},
  author = {Chulkwang Kwak},
  journal= {arXiv preprint arXiv:1708.00127},
  year   = {2018}
}

Comments

38 pages, final version, some typos and an error in (3.40) are revised, accepted for publication in JMAA

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