Abstract
We study the deformed Hunter–Saxton equation proposed by Manna and Neveu (2003 Preprint physics/0303085). It is known that the Manna–Neveu system is integrable admitting a Lax pair. In this paper, we show that this equation can be explained as an equation of the geodesic flow associated with a right-invariant metric on the Bott–Virasoro group. We also discuss the bi-Hamiltonian structure of the deformed Hunter–Saxton equation.
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