Polynomial deceleration for a system of cubic nonlinear Schrodinger equations in one space dimension

被引：2

作者：

Kita, Naoyasu ^{[1
]}

Masaki, Satoshi ^{[2
]}

Segata, Jun-ichi ^{[3
]}

Uriya, Kota ^{[4
]}

机构：

[1] Kumamoto Univ, Fac Adv Sci & Technol, Kumamoto 8608555, Japan

[2] Osaka Univ, Grad Sch Engn Sci, Dept Syst innovat, Toyonaka, Osaka 5608531, Japan

[3] Kyushu Univ, Fac Math, Fukuoka 8190395, Japan

[4] Okayama Univ Sci, Fac Sci, Dept Appl Math, Okayama 7000005, Japan

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2023年 / 230卷

关键词：

Nonlinear Schrodinger equation; Asymptotic behavior of solutions; Long range scattering; LONG-RANGE SCATTERING; ASYMPTOTIC-BEHAVIOR; TIME ASYMPTOTICS; BLOWUP; BOUNDS; NLS;

D O I：

10.1016/j.na.2023.113216

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the initial value problem of a specific system of cubic nonlinear Schrodinger equations. Our aim of this research is to specify the asymptotic profile of the solution in L infinity as t -> infinity. It is then revealed that the solution decays slower than a linear solution does. Further, the difference of the decay rate is a polynomial order. This deceleration of the decay is due to an amplification effect by the nonlinearity. This nonlinear amplification phenomena was previously known for several specific systems, however the deceleration of the decay in these results was by a logarithmic order. As far as we know, the system studied in this paper is the first model in that the deceleration in a polynomial order is justified.(c) 2023 Elsevier Ltd. All rights reserved.

引用

页数：22

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