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

Chulkwang Kwak

doi:10.1016/j.jmaa.2018.01.040

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

Chulkwang Kwak

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

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(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 language	English
Pages (from-to)	1327-1364
Number of pages	38
Journal	Journal of Mathematical Analysis and Applications
Volume	461
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2018.01.040
State	Published - 15 May 2018

Bibliographical note

Publisher Copyright:
© 2018 Elsevier Inc.

Keywords

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

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10.1016/j.jmaa.2018.01.040

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title = "Periodic fourth-order cubic NLS: Local well-posedness and non-squeezing property",

abstract = "In this paper, we consider the cubic fourth-order nonlinear Schr{\"o}dinger 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].",

keywords = "Fourth-order NLS, Local well-posedness, Non-squeezing property, Wick ordered NLS",

author = "Chulkwang Kwak",

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doi = "10.1016/j.jmaa.2018.01.040",

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T1 - Periodic fourth-order cubic NLS

T2 - Local well-posedness and non-squeezing property

AU - Kwak, Chulkwang

PY - 2018/5/15

Y1 - 2018/5/15

N2 - 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].

AB - 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].

KW - Fourth-order NLS

KW - Local well-posedness

KW - Non-squeezing property

KW - Wick ordered NLS

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DO - 10.1016/j.jmaa.2018.01.040

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SN - 0022-247X

VL - 461

SP - 1327

EP - 1364

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

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

Abstract

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Keywords

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