Liouville correspondence between the Short-Pulse Hierarchy and the   Sine-Gordon Hierarchy
  This paper considers the whole hierarchy of bi-Hamiltonian integrable equations associated to each of the Short-Pulse (SP) equation and the Sine-Gordon (SG) equation. We prove that the transformation that relates the SP equation with the SG equation also serves to establish the correspondence between their flows and Hamiltonian conservation laws in respective hierarchy. 
Jing Kang and Xiaochuan Liu
nlin.SI