  The Neumann and Chaplygin systems on the sphere are simultaneously separable
in variables obtained from the standard elliptic coordinates by the proper
Backlund transformation. We also prove that after similar Backlund
transformations other curvilinear coordinates on the sphere and on the plane
become variables of separations for the system with quartic potential, for the
Henon-Heiles system and for the Kowalevski top. It allows us to say about some
analog of the hetero Backlund transformations relating different
Hamilton-Jacobi equations.
