Boson stars as solitary waves
2007 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 274, no 1, 1-30 p.Article in journal (Refereed) Published
We study the nonlinear equation i theta t psi = (root-Delta+m(2) - m) psi - (vertical bar x vertical bar(-1) * vertical bar psi vertical bar(2)) psi on R-3, which is known to describe the dynamics of pseudo-relativistic boson stars in the meanfield limit. For positive mass parameters, m > 0, we prove existence of travelling solitary waves, psi(t, x) = ei t mu phi(v)(x - vt), for some mu is an element of R and with speed vertical bar v vertical bar < 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 phi(v) H-1/2(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(v)(x - vt) and pointwise exponential decay of phi(v)(x) in x.
Place, publisher, year, edition, pages
2007. Vol. 274, no 1, 1-30 p.
IdentifiersURN: urn:nbn:se:kth:diva-16781DOI: 10.1007/s00220-007-0272-9ISI: 000247929400001ScopusID: 2-s2.0-34249318542OAI: oai:DiVA.org:kth-16781DiVA: diva2:334824
QC 201005252010-08-052010-08-05Bibliographically approved