Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 73, pp. 1-12.

Title: Travelling solitary waves for boson stars

Authors: Guoqing Zhang (Univ. of Shanghai for Science and Tech., Shanghai, China)
         Ningning Song (Univ. of Shanghai for Science and Tech., Shanghai, China)

Abstract:
 In this article, we study the pseudo-relativistic Hartree equation
 $$
 i\partial_{t}\psi=(\sqrt{-\Delta+m^2}-m)\psi
 -(\frac{e^{-\mu|x|}}{4\pi|x|}\ast|\psi|^2)\psi,\quad \text{on }\mathbb{R}^3,
 $$
 which describes the dynamics of pseudo-relativistic boson stars with
 rest mass $m>0$ in the mean-field limit.
 Based on Ekeland variational principle, concentration-compactness
 lemma and Gagliardo-Nirenberg inequality, we prove existence of travelling
 solitary waves under the critical stellar mass.
 In addition to their existence, we obtain orbital stability 
 by using a general idea presented in Cazenave and Lions [2].

Submitted July 3, 2018. Published May 28, 2019.
Math Subject Classifications: 35Q40, 35Q55, 47J35.
Key Words: Travelling solitary wave; boson star equation; critical stellar mass.