  It is well known that Jackiw-Teitelboim (JT) gravity posses the simplest
theory on 2-dimensional gravity. The model has been fruitfully studied in
recent years. In the present work, we investigate exact solutions for both JT
and deformed JT gravity recently proposed in the literature. We revisit exact
Euclidean solutions for Jackiw-Teitelboim gravity using all the non-zero
components of the dilatonic equations of motion using proper integral
transformation over Euclidean time coordinate. More precisely, we study exact
solutions for hyperbolic coverage, cusp geometry and another compact sector of
the AdS$_2$ spacetime manifold.
