Local well-posedness for the nonlinear Schr\"odinger equation with harmonic potentila in $H^s$
Bull. Korean Math. Soc. 2011 Vol. 48, No. 6, 1291-1302
https://doi.org/10.4134/BKMS.2011.48.6.1291
Published online November 1, 2011
Shan Zhang, Zuhan Liu, and Zhongxue L\"u
Yangzhou University, Xuzhou Normal University, Xuzhou Normal University
Abstract : We establish the local well-posedness for the Cauchy problem of the nonlinear Schr\"{o}dinger equation with harmonic potential in $H^{s}(\mathbb{R}^{n})$, where $s\in \mathbb{R},~ s>0.$
Keywords : nonlinear Schr\"odinger equation
MSC numbers : 5Q55, 35A05
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