The kernel condition of a linearized pseudo-relativistic Hartree equation, a numerical approach
2009 (English)In: MATHEMATICAL MODELING OF WAVE PHENOMENA / [ed] Nilsson B; Fishman L; Karlsson A; Nordebo S, 2009, Vol. 1106, 173-180 p.Conference paper (Refereed)
We consider the nonlinear equation i partial derivative(t)psi = (root-Delta+m(2) - m)psi - (vertical bar x vertical bar(-1) * vertical bar psi vertical bar(2))psi on R-3 describing the dynamics of pseudo-relativistic boson stars in the mean-field limit. Recently this equation, with an external potential has been used to describe the dynamics of boson stars under the influence of an external gravitational field. This analysis makes one explicit critical assumption. To the above differential equation we call associate all energy function. The assumption is on the size of the kernel of the Hessian of the energy functional when it is linearized around a soliton, In this paper we provide a numerical indicator that the assumption is satisfied. To achieve this goal. we need to numerically calculate the soliton for a range of normalized frequencies as well as and the spectrum of the linearization around a soliton of the Euler-Lagrange equations describing the minimizer.
Place, publisher, year, edition, pages
2009. Vol. 1106, 173-180 p.
, AIP CONFERENCE PROCEEDINGS, ISSN 0094-243X ; 1106
Boson star, pseudo-relativistic Hartree equation, Petviashvili iteration, non-linear ground state
Engineering and Technology
IdentifiersURN: urn:nbn:se:kth:diva-31217DOI: 10.1063/1.3117092ISI: 000264867300019ScopusID: 2-s2.0-65649134704OAI: oai:DiVA.org:kth-31217DiVA: diva2:406221
3rd Conference on Mathematical Modeling of Wave Phenomena/20th Nordic Conference on Radio Science and Communications, Växjö, SWEDEN, JUN 13-19, 2008
QC 201103252011-03-252011-03-112011-03-25Bibliographically approved