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

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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 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 [36] and [27], and to prove the latter we used the ideas in [8].

Original languageEnglish
Pages (from-to)1327-1364
Number of pages38
JournalJournal of Mathematical Analysis and Applications
Volume461
Issue number2
DOIs
StatePublished - 15 May 2018

Keywords

  • Fourth-order NLS
  • Local well-posedness
  • Non-squeezing property
  • Wick ordered NLS

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