Mapping of solutions of the Hamilton-Jacobi equation by an arbitrary   canonical transformation
  It is shown that given an arbitrary canonical transformation and an arbitrary Hamiltonian, there is a naturally defined mapping that sends any solution of the Hamilton-Jacobi (HJ) equation into a solution of the HJ equation corresponding to the new Hamiltonian 
G.F. Torres del Castillo, H.H. Cruz Dom\'inguez, A. de Yta   Hern\'andez, J.E. Herrera Flores, and A. Sierra Mart\'inez
physics.class-ph