Linearization of the Relativistic Oscillator Hierarchy
  This paper is based on MacColl's [1] solution of the equation of motion for a linear (harmonic) oscillator subject to the laws of special relativity in the rest frame of the center of attraction. MacColl's result can be extended to the quartic oscillator in this frame with one extremely simple adjustment of the linearization map given in Anderson [2]. In fact, it can be extended to all the attractive oscillators in this frame. 
Robert L. Anderson
physics.class-ph