If you just want your current jQuery UI code to work with touch events, you can use the jQuery UI Touch Punch monkey patch.
The only "technical problem or core incompatibility" is that jQuery UI (1.x) only listens for mouse events, not touch events (See @ScottGonzales's response for the historical reason). jQuery touch punch, above, makes that change. You can even try some of the jQuery UI examples on that page, and they work. Generally, using Touch Punch is the currently accepted solution.
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