• Corpus ID: 233864907

# Scattering of the three-dimensional cubic nonlinear Schr\"odinger equation with partial harmonic potentials

@inproceedings{Cheng2021ScatteringOT,
title={Scattering of the three-dimensional cubic nonlinear Schr\"odinger equation with partial harmonic potentials},
author={Xing Cheng and Chang-Yu Guo and Zihua Guo and Xian Liao and Jia Shen},
year={2021}
}
• Published 6 May 2021
• Mathematics
In this paper, we consider the following three dimensional defocusing cubic nonlinear Schr\"odinger equation (NLS) with partial harmonic potential \begin{equation*}\tag{NLS} i\partial_t u + \left(\Delta_{\mathbb{R}^3 }-x^2 \right) u = |u|^2 u, \quad u|_{t=0} = u_0. \end{equation*} Our main result shows that the solution $u$ scatters for any given initial data $u_0$ with finite mass and energy. The main new ingredient in our approach is to approximate (NLS) in the large-scale case by a relevant…
5 Citations
Riesz transforms and Sobolev spaces associated to the partial harmonic oscillator
• Mathematics
• 2022
. In this paper, our goal is to establish the Sobolev space associated to the partial harmonic oscillator. Based on its heat kernel estimate, we ﬁrstly give the deﬁnition of the fractional powers of
On scattering for generalized NLS on waveguide manifolds
• Mathematics
• 2022
. In this paper, we prove the large data scattering for fractional nonlinear Schr¨odinger equations (FNLS) on waveguide manifolds R d × T , d ≥ 3. This result can be regarded as the fractional
Global well-posedness and scattering of the two dimensional cubic focusing nonlinear Schr\"odinger system
• Mathematics
• 2022
In this article, we prove the global well-posedness and scattering of the cubic focusing infinite coupled nonlinear Schrödinger system on R below the threshold in L2xh (R × Z). We first establish the
On the decay property of the cubic fourth-order Schr\"odinger equation
• Mathematics
• 2022
In this short paper, we prove that the solution of the cubic fourth-order Schrödinger equation (4NLS) on R (5 ≤ d ≤ 8) enjoys the same (pointwise) decay property as its linear solution does. This
Fermi-Pasta-Ulam phenomena and persistent breathers in the harmonic trap.
• Physics
Physical review. E
• 2021
This work identifies Fermi-Pasta-Ulam-like recurrence phenomena, whereby the normal-mode spectrum passes in close proximity of the initial configuration, and two-mode states with time-independent mode amplitude spectra that translate into long-lived breathers of the original NLS equation.