The Xperia Sola isn't slated for a Jelly Bean update, but the folks at xda-developers.com have succeeded where others failed.
This was an understandable omission considering the measly 512MB RAM on the Sola.
This didn’t deter the folks at xda-developers.com however and they succeeded in porting the stock Jelly Bean build from the Xperia U to the Xperia Sola.
You can get detailed info on the XDA forums over here.
Make sure to follow the instructions to the letter to avoid bricking your device. We’ve tried it out ourselves and the process shouldn’t take longer than 15-20 minutes, at most, if you have the requisite files already downloaded.