General Solution of the WZNW System and 2D Induced Gravity in Curved Space-time

We find the general solution of the equations of motion for the WZNW system in curved space-time for arbitrary external gauge fields. Using the connection between the WZNW system for $SL(2,R)$ group and 2D induced gravity we obtain the general solution of the equations of motion for 2D induced gravity in curved space-time from that of the WZNW system. We independently presented the direct solution of 2D induced gravity equations of motion and obtain the same result.