Euler Equations of the Generalized Bott-Virasoro Group

In this paper, we will generalize the Bott-Virasoro group, applying the concept of the connection cochain, and derive the Euler equations corresponding to the generalized Bott-Virasoro group. We will show the relationships between the new Euler equations and the old ones. Moreover, we will study the geodesic equation corresponding to the Burgers equation and apply it to the exponential curve.