Boson Stars as Solitary Waves
| dc.creator | Froehlich, Juerg | |
| dc.creator | Jonsson, B. Lars G. | |
| dc.creator | Lenzmann, Enno | |
| dc.date | 2005-12-12 | |
| dc.date.accessioned | 2026-07-07T10:46:36Z | |
| dc.date.available | 2026-07-07T10:46:36Z | |
| dc.description | We study the nonlinear equation $i \partial_t ψ= (\sqrt{-Δ+ m^2} - m) ψ- ( |x|^{-1} \ast |ψ|^2 ) ψ$ on $\RR^3$, 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, $ψ(t,x) = e^{i t μ} \sol_{v}(x-vt)$, 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 $\sol_v \in \Hhalf(\RR^3)$ 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 $ψ(t,x) = e^{it μ} \sol_v(x-vt)$ and pointwise exponential decay of $\sol_v(x)$ in $x$. | |
| dc.description | 30 pages | |
| dc.identifier | https://arxiv.org/abs/math-ph/0512040 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0512040 | |
| dc.identifier | Commun.Math.Phys.274:1-30,2007 | |
| dc.identifier | doi:10.1007/s00220-007-0272-9 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/183290 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q55; 49J40; 81Q05 | |
| dc.title | Boson Stars as Solitary Waves | |
| dc.type | text |