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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:461

Article

Kwak, Chulkwang¹ 

[1] Pontificia Univ Catolica Chile, Fac Matemat, Campus San Joaquin,Avda Vicuna Mackenna 4860, Santiago, Chile

关键词: Fourth-order NLS;    Wick ordered NLS;    Local well-posedness;    Non-squeezing property;   

DOI  :  10.1016/j.jmaa.2018.01.040

来源: Elsevier

【 摘 要 】

In this paper, we consider the cubic fourth-order nonlinear Schrodinger 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 L-2(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]. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free