Travelling-wave-type and stationary soliton solutions of the Brans–Dicke equation

Abstract

Introducing the Lax pair, it is shown that the Brans–Dicke equation is integrable for space-times with two commuting Killing vectors. Using the inverse-scattering method given by Belinskii and Zakharov, the n soliton solutions for the case of the time-dependent metric are introduced. Specially, the one and two travelling-wave-type solitonic solutions are obtained. Also it is shown that the method could be applied to the case of stationary axially symmetric space-times with two commuting Killing vectors. PACS Nos.: 04.20jb, 04.50+h