Zobrazeno 1 - 10
of 357
pro vyhledávání: '"Zhao, Zehua"'
We investigate the long time dynamics of the nonlinear Schr\"odinger equation (NLS) with combined powers on the waveguide manifold $\mathbb{R}^d\times\mathbb{T}$. Different from the previously studied NLS-models with single power on the waveguide man
Externí odkaz:
http://arxiv.org/abs/2409.15860
In this article, we study the scattering theory for the two dimensional defocusing quintic nonlinear Schr\"odinger equation(NLS) with partial harmonic oscillator which is given by \begin{align}\label{NLS-abstract} \begin{cases}\tag{PHNLS} i\partial_t
Externí odkaz:
http://arxiv.org/abs/2409.09789
We continue our study of bilinear estimates on waveguide $\mathbb{R}\times \mathbb{T}$ started in \cite{DFYZZ2024,Deng2023}. The main point of the current article is, comparing to previous work \cite{Deng2023}, that we obtain estimates beyond the sem
Externí odkaz:
http://arxiv.org/abs/2407.05654
We prove dispersive decay, pointwise in time, for solutions to the mass-critical nonlinear Schr\"odinger equation in spatial dimensions $d=1,2,3$.
Externí odkaz:
http://arxiv.org/abs/2403.09989
We study local-in-time and global-in-time bilinear Strichartz estimates for the Schr\"odinger equation on waveguides. As applications, we apply those estimates to study global well-posedness of nonlinear Schr\"odinger equations on these waveguides.
Externí odkaz:
http://arxiv.org/abs/2402.02916
The wide dissemination of fake news has affected our lives in many aspects, making fake news detection important and attracting increasing attention. Existing approaches make substantial contributions in this field by modeling news from a single-moda
Externí odkaz:
http://arxiv.org/abs/2306.15231
In this paper, we prove Strichartz estimates for many body Schr\"odinger equations in the periodic setting, specifically on tori $\mathbb{T}^d$, where $d\geq 3$. The results hold for both rational and irrational tori, and for small interacting potent
Externí odkaz:
http://arxiv.org/abs/2304.00882
We consider the periodic cubic-quintic nonlinear Schr\"odinger equation \begin{align}\label{cqnls_abstract} (i\partial_t +\Delta )u=\mu_1 |u|^2 u+\mu_2 |u|^4 u\tag{CQNLS} \end{align} on the three-dimensional torus $\mathbb{T}^3$ with $\mu_1,\mu_2\in
Externí odkaz:
http://arxiv.org/abs/2301.13433
Autor:
Zhao, Zehua
In this short paper, we prove Strichartz estimates for N-body Schr\"odinger equations in the waveguide manifold setting (i.e. on semiperiodic spaces $\mathbb{R}^m\times \mathbb{T}^n$ where $m\geq 3$), provided that interaction potentials are small en
Externí odkaz:
http://arxiv.org/abs/2301.13429
In this paper we discuss quantitative (pointwise) decay estimates for solutions to the 3D cubic defocusing Nonlinear Schr\"odinger equation with various initial data, deterministic and random. We show that nonlinear solutions enjoy the same decay rat
Externí odkaz:
http://arxiv.org/abs/2211.03124