ON THE CAUCHY PROBLEM OF A COHERENTLY COUPLED SCHRÖDINGER SYSTEM

doi:10.1016/S0252-9602(16)30006-6

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (2): 371-384.doi: 10.1016/S0252-9602(16)30006-6

ON THE CAUCHY PROBLEM OF A COHERENTLY COUPLED SCHRÖDINGER SYSTEM

王忠, 崔尚斌

Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China

收稿日期:2013-12-11 修回日期:2015-08-06 出版日期:2016-04-25 发布日期:2016-04-25
作者简介:Zhong WANG,E-mail:wangzh79@mail2.sysu.edu.cn;Shangbin CUI,E-mail:cuishb@mail.sysu.edu.cn
基金资助:
This work is supported by the China National Natural Science Foundation under grant number 11171357.

ON THE CAUCHY PROBLEM OF A COHERENTLY COUPLED SCHRÖDINGER SYSTEM

Zhong WANG, Shangbin CUI

Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China

Received:2013-12-11 Revised:2015-08-06 Online:2016-04-25 Published:2016-04-25
Supported by:
This work is supported by the China National Natural Science Foundation under grant number 11171357.

摘要/Abstract

摘要：

In this article, we consider the well-posedness of a coherently coupled Schrödinger system with four waves mixing in space dimension n≤4. The Cauchy problem for the cubic system is studied in L² for n≤2 and in H¹ for n≤4. We obtain two sharp conditions between global existence and blow up.

关键词: Cauchy problem, coherently, Schrödinger system, global existence

Abstract:

Key words: Cauchy problem, coherently, Schrödinger system, global existence

中图分类号:

35A05

王忠, 崔尚斌. ON THE CAUCHY PROBLEM OF A COHERENTLY COUPLED SCHRÖDINGER SYSTEM[J]. 数学物理学报(英文版), 2016, 36(2): 371-384.

Zhong WANG, Shangbin CUI. ON THE CAUCHY PROBLEM OF A COHERENTLY COUPLED SCHRÖDINGER SYSTEM[J]. Acta mathematica scientia,Series B, 2016, 36(2): 371-384.

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ON THE CAUCHY PROBLEM OF A COHERENTLY COUPLED SCHRÖDINGER SYSTEM

ON THE CAUCHY PROBLEM OF A COHERENTLY COUPLED SCHRÖDINGER SYSTEM

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