ON THE CAUCHY PROBLEM FOR A NONLOCAL NONLINEAR SCHRODINGER EQUATION

被引：0

作者：

Wang, Hongwei ^{[1
]}

Esfahani, Amin ^{[2
]}

机构：

[1] Anyang Normal Univ, Sch Math & Stat, Anyang, Peoples R China

[2] Nazarbayev Univ, Dept Math, Nur Sultan 010000, Kazakhstan

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2022年 / 27卷 / 12期

关键词：

Schrodinger equation; Well-posedness; Standing wave; ILL-POSEDNESS; WELL-POSEDNESS; MODULATION;

D O I：

10.3934/dcdsb.2022039

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper considers the one-dimensional Schrodinger equation with nonlocal nonlinearity that describes the interactions of nonlinear disper-sive waves. We obtain some the local well-posedness and ill-posedness result associated with this equation in the Sobolev spaces. Moreover, we prove the existence of standing waves of this equation. As corollary, we derive the con-ditions under which the solutions are uniformly bounded in the energy space.

引用

页码：7185 / 7206

页数：22

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