Seutonius writes that Augustus delayed at Brundisium for twenty seven days - just long enough to satisfy the demands of the soldiers - before moving to Anatolia, Syria, then Egypt, to take Alexandria.
What is the reason for this delay? What demands would the soldiers have had? I'm constructing an essay on the machinations and manipulation of Augustus during the Principate - the manipulation of the senate, people and armies. I think this may fit in to the latter, if the reason is for what I think it is (allow the soldiers to enjoy themselves before going to war.)
Are there any major ways that Augustus used manipulation to control the three above factions in order to establish his Empire?
You are referring to his quick return to Italy late in 31 BCE, after the Battle of Actium. The twenty-seven days was not so much a delay, but rather the opposite: it was a very quick trip to Italia to assuage the fears of the Roman populace, and, more importantly, the soldiers. He deliberately went no further than Brundisium because it indicated to all that he did not intend to stay very long before returning to his business in the East.
A large contingent of soldiers had been sent back to Italy after Actium and told to billet at Brundisium and to await further instructions. These included both Octavian's own forces as well as those who had deserted to him from Antonius' side before or during the battle(s) of the past year. The assumption was that these soldiers (of both types) would be discharged and settled (given land), now that the war was over and there was no serious obstacle left standing to Octavian's political domination. We don't know for sure what their precise problems were, but at the very least they were probably agitated with the delays and ready to go home rather than living in temporary barracks at the port.
The prospect of soldier settlements was alarming for the Roman people. Settling even a few legions in Italia meant a lot of upheaval, hurt feelings, "stolen" land, etc. It is important to emphasizethat there were so many soldiers after Actium. Dozens and dozens of legions. So Octavian went back to Brundisium and decided the best course was to "buy" land for this first wave of settlements (eventually the other waves would be sent to colonies in North Africa, Spain, Gaul, and many other places). He didn't have money to buy that much land, but he was on his way to Egypt and probably counted on finding the funds there. So he borrowed on the future and got the ball rolling on the settlement of this first wave, which had been stewing at Brundisium.
As far as your paper: settlement/disbanding of soldiers was a constant problem in the Late Republic, and came to be the responsibility of the commander. Where to put them? Whom to displace? Etc. Already we see problems with this process as far back as Sulla, and Pompey certainly wrestled with it as well. What Octavian is doing here in winter of 31 at Brundisium was nothing new. I suppose he rightly recognized that tens (eventually hundreds) of thousands of discontented soldiers was a problem that needed his immediate attention and was worth the quick trip back to Italia.
Will Broadhead has a nice summary of land distribution in A Companion to the Roman Army (ed Erdkamp 2007), though he spends a lot of time talking about the middle Republic and stops before Actium. Still, he has good things to say about the Late Republican trends leading up to Octavian's settlements.