Statistical mechanics of nonlinear wave equations. 3. Metric transitivity for hyperbolic sine-gordon

McKean and Vaninsky proved that the canonical measure e^-Hd^∞Q d^∞P based upon the Hamiltonian {Mathematical expression} of the wave equation ∂²Q/∂t² - ∂²Q/∂x² +f(Q) = 0 with restoring force f(Q)=F'(Q) is preserved by the associated flow of Q and P =Q^{{dot operator}}, and they conjectured that metric transitivity prevails, always on the whole line, and likewise on the circle unless f(Q)=Q or f(Q)=sh Q. Here, the metric transitivity is proved for the whole line in the second case. The proof employs the beautiful "d'Alembert formula" of Krichever.