The nonlinear Schrödinger equations with harmonic potential in modulation spaces

2018/10/15 by Bhimani, Divyang G.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.06556

Abstract

We study nonlinear Schrödinger i∂_tu-Hu=F(u) (NLSH) equation associated to harmonic oscillator H=-Δ+|x|² in modulation spaces M^p,q. When F(u)= (|x|^-γ∗ |u|²)u, we prove global well-posedness for (NLSH) in modulation spaces M^p,p(\mathbb R^d) (1≤ p < 2d/(d+γ), 0

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