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The Liouville correspondence between the short-pulse integrable hierarchy and the sine-Gordon integrable hierarchy is studied. It is shown that the transformation relating the short-pulse equation with the sine-Gordon equation also establishes the correspondence between their flows and Hamiltonian conservation laws in respective hierarchy. This proposes an alternative approach to derive the Hamiltonian conservation laws of the short-pulse equation from the known ones of the classical sine-Gordon equation.

Liouville Correspondence Between the Short-Pulse Hierarchy and the Sine-Gordon Hierarchy