Dilatations and the Conformal Group Are Treated in the Recent Report by H. Dreyer.
http://edu.itp.phys.ethz.ch/fs13/cft/CGIVD2_Dreyer.pdf

has been cited by the following article:

• TITLE: A Note on the Lie Algebra of the Invariants in the CBS Nonlinear Equation

  AUTHORS: Jose M. Cerveró

  KEYWORDS: Nonlinear Integrability, Group Theory, Weierstrass P-Elliptic Function

  JOURNAL NAME: Journal of Modern Physics, Vol.9 No.6, May 25, 2018

  ABSTRACT: In this short note, a particular realization of the vector fields that form a Lie Algebra of symmetries for the Calogero-Bogoyavleskii-Schiff equation is found. The Lie Algebra is examined and the result is a semidirect product of two Lie Groups. The structure of the semidirect product is examined through the table of commutation rules. Two reductions are made with the help of two sets of generators and the final outcome for the solution is related to the elliptic Painlevé P(ξ)-function.