Is there anyway I can install Ubuntu for Android alongside android by dual-booting it? is it compatible with Xperia U?
Xperia U has
NovaThor U8500 chipset
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No. Ubuntu alongside android was not released. Most probably ubuntu edge going to be the first device (if the funding success).
The closest one is available now is ubuntu touch. This is not alongside Android. It is complete replacement of android. Regarding support see What hardware does Ubuntu Touch support?
Ubuntu touch installation is possible only if there is CM10 build (the lower level abstraction ) is available & Bootloader is unlocked.
If the above conditionis met , the you need to port the image. For porting see ubuntu touch porting guide. see https://wiki.ubuntu.com/Touch/Devices
Though the device list already include s4, those will not work for your device as the hardware is different and so as the drivers.