Seen and heard of a few similar injuries over the years - a few due to parachute jumps - but most from jumping or falling from height.
If you're getting physio, stick with their advice and don't try and hurry the recovery. If you start getting pins and needles or numbness in you lower limbs get back in touch with neuro team....
If the fracture remains unstable or is a risk to the spinal cord, stabilisation surgery may be an option, but try and avoid that if possible, good luck with recovery.