From Sonic Retro
Sonic Advance series
In the Game Boy Advance games, the Jump Dash is one of Sonic the Hedgehog's moves, activated by pressing or twice in rapid succession after jumping. Sonic does a sudden jumping dash forwards, gaining a lot of momentum. This move leaves Sonic vulnerable, so use with caution. It finds its greatest application in speedruns.
Shadow the Hedgehog
In Shadow's game, Jump Dash allows the black hedgehog to walk on walls for short distances. It is sometimes needed to cross short gaps. The player must jump on to a wall with Homing Attack to use it. Shadow can move forward with the control stick. It can also be used during Triangle Jump. But unlike Triangle Jump, only one wall is needed to perform Jump Dash.
Untargeted Homing Attack
The term "Jump Dash" is also used by some players, and by Omochao in Sonic Adventure 2, to refer to the boost of speed which can be obtained by performing a Homing Attack when no enemies are within range. Usually this causes the player to dart forwards in midair with a burst of forward momentum, much like the Sonic Advance move; although here Sonic remains rolled up in a ball.