Ricci Solitons on the Poincaré upper half plane

In this paper, we characterize the Ricci soliton equations on the Poincaré upper half plane . First we classify all Ricci soliton and Ricci Bourguignon soliton in the half plane of Poincaré and after we generalize those equations in ${\mathbb{H}}^n$. We obtain some nice properties of the soliton about their geodesic flows.