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Mat. Zametki, 2009, Volume 86, Issue 5, Pages 686–691 (Mi mz8512)  

This article is cited in 1 scientific paper (total in 1 paper)

Global Existence for a System of Weakly Coupled Nonlinear Schrödinger Equations

Ji Shu, Jian Zhang

Sichuan University, Department of Mathematics

Abstract: This paper discusses the weakly coupled nonlinear Schrödinger equations in the supercritical case. With the best constant of Gagliardo–Nirenberg inequality, we derive a sufficient condition for the global existence of the solutions; this condition is expressed in terms of the stationary solutions (nonlinear ground state).

Keywords: weakly coupled nonlinear Schrödinger equations, global existence, Gagliardo–Nirenberg inequality, Cauchy problem, Laplace operator, nonlinear optics

DOI: https://doi.org/10.4213/mzm8512

Full text: PDF file (425 kB)
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English version:
Mathematical Notes, 2009, 86:5, 650–654

Bibliographic databases:

UDC: 517.958
Received: 12.07.2008

Citation: Ji Shu, Jian Zhang, “Global Existence for a System of Weakly Coupled Nonlinear Schrödinger Equations”, Mat. Zametki, 86:5 (2009), 686–691; Math. Notes, 86:5 (2009), 650–654

Citation in format AMSBIB
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\by Ji Shu, Jian Zhang
\paper Global Existence for a System of Weakly Coupled Nonlinear Schr\"{o}dinger Equations
\jour Mat. Zametki
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\vol 86
\issue 5
\pages 686--691
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\transl
\jour Math. Notes
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\vol 86
\issue 5
\pages 650--654
\crossref{https://doi.org/10.1134/S0001434609110078}
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    This publication is cited in the following articles:
    1. Ceccon J., Duran C.E., “Sharp Constants in Riemannian l-P-Gagliardo-Nirenberg Inequalities”, J. Math. Anal. Appl., 433:1 (2016), 260–281  crossref  mathscinet  zmath  isi  scopus
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