Boson Stars as Solitary Waves期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Boson Stars as Solitary Waves

Authors:

Jürg Fröhlich B Lars G Jonsson Enno Lenzmann

Institution:

(1) Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland;(2) Division of Electromagnetic Engineering, School of Electrical Engineering, Royal Insitute of Technology, SE-100 44 Stockholm, Sweden;(3) Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland;(4) Department of Mathematics, MIT, Cambridge, MA 02139, USA

Abstract:

We study the nonlinear equation

$i \partial_t \psi = (\sqrt{-\Delta + m^2} - m)\psi - ( |x|^{-1} \ast |\psi|^2 ) \psi \quad {\rm on}\,\mathbb{R}^3$

which is known to describe the dynamics of pseudo-relativistic boson stars in the mean-field limit. For positive mass parameters, m > 0, we prove existence of travelling solitary waves, $\psi(t,x) = e^{{i}{t}\mu} \varphi_{v}(x - vt)$ , for some $\mu \in {\mathbb{R}}$ and with speed |v| < 1, where c = 1 corresponds to the speed of light in our units. Due to the lack of Lorentz covariance, such travelling solitary waves cannot be obtained by applying a Lorentz boost to a solitary wave at rest (with v = 0). To overcome this difficulty, we introduce and study an appropriate variational problem that yields the functions $\varphi_v \in {\bf H}^{1/2}({\mathbb{R}}^3)$ as minimizers, which we call boosted ground states. Our existence proof makes extensive use of concentration-compactness-type arguments. In addition to their existence, we prove orbital stability of travelling solitary waves $\psi(t, x) = e^{{i}{t}\mu}\varphi_v(x - vt)$ and pointwise exponential decay of $\varphi_v(x)$ in x.

Keywords:

本文献已被 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏