ON THE CAUCHY PROBLEM OF A COHERENTLY COUPLED SCHRODINGER SYSTEM

ON THE CAUCHY PROBLEM OF A COHERENTLY COUPLED SCHRODINGER SYSTEM

In this article, we consider the well-posedness of a coherently coupled Schrodinger system with four waves mixing in space dimension n ≤ 4. The Cauchy problem for the cubic system is studied in L^2 for n ≤ 2 and in H^1 for n ≤ 4. We obtain two sharp conditions between global existence and blow up....

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Veröffentlicht in:Acta mathematica scientia 2016-03, Vol.36 (2), p.371-384
1. Verfasser: 王忠 崔尚斌
Format: Artikel
Sprache:eng
Schlagworte:
35A05
35B65
Cauchy problem
Coherence
coherently
global existence
Joining
Schroedinger equation
Schrödinger system
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Zusammenfassung:In this article, we consider the well-posedness of a coherently coupled Schrodinger system with four waves mixing in space dimension n ≤ 4. The Cauchy problem for the cubic system is studied in L^2 for n ≤ 2 and in H^1 for n ≤ 4. We obtain two sharp conditions between global existence and blow up.
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(16)30006-6