修正一维Schrödinger方程的全局解

Pub Date : 2021-06-01 DOI:10.4208/cmr.2021-0015

Ting Zhang

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引用次数: 3

摘要

在本文中，我们考虑改进的一维Schrödinger方程:(Dt−F(D)) u=λ|u|u，其中F(ξ)是一个二阶常系数经典椭圆符号，初始基准面尺寸为ε≪1。结合向量场方法和Delort引入的半经典分析方法，证明了其解是全局的。此外，当t→+∞时，我们得到了u的一项渐近展开式。AMS学科分类:初级:35Q55;次级:35A01、35B40、35S50

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Global Solutions of Modified One-Dimensional Schrödinger Equation

In this paper, we consider the modified one-dimensional Schrödinger equation: ( Dt−F(D) ) u=λ|u|u, where F(ξ) is a second order constant coefficients classical elliptic symbol, and with smooth initial datum of size ε≪1. We prove that the solution is global-intime, combining the vector fields method and a semiclassical analysis method introduced by Delort. Moreover, we get a one term asymptotic expansion for u when t→+∞. AMS subject classifications: Primary: 35Q55; Secondary: 35A01, 35B40, 35S50

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