How was Alexanders army able to deal with the Persian archers?

[Miaow]

It should be noted from what i've read that experienced Roman generals like Africanus sometimes forgone the traditional manipular formations (specially having the youth up front etc) Forgoing massive reserves of replacement men to create a stronger main battle line. The 2nd Punic wars did force the romans to adopt new tactics.

While the manipular formation was in many instances a boon to the Romans, it was a main cause of their defeat at Cannae. The Roman narrow, deep formation made it easy for the numerically inferior Carthaginians to envelop them.

On the topic of Greeks against Persians, let's not forget that the Persians initially defeated the Greeks they met in Asia—the Ionian, Aeolian etc colonies—with relative ease, to the extent that contemporary Greek sources insist that, prior to Marathon, the Greeks essentially pissed themselves with fear at the idea of fighting Persians. That's why so few Greeks were willing to help Athens with the first invasion; only the Plataeans, who would have been enslaved by the Thebans without Athens, and the Spartans, who feared dishonour more than death, were willing to come (and only the Plataeans were there on time).

Indeed, the whole reason that the Persians were attacking Athens wasn't that they were horrible evil people intent on enslaving the "free world", but that Athens had supported its Ionian colonies in rebelling against the Persians. The Persians had crushed that Greek rebellion, and wanted to take revenge on what they saw as a foreign power meddling in their internal affairs. Well, they also wanted to conquer the whole world too, but the reason they targeted Athens when they did was that Athens had been unsuccessfully attacking them.

As to why the Persians went from beating the snot out of hoplites to having the snot beaten out of them by hoplites, one of the major reasons was cavalry—specifically the logistics of cavalry. The descriptions of some EB units reflect that effective cavalry required rather alot more horses than men, and horses are difficult at best to transport by sea. Moreover, Greece being Greece, it was very difficult for the Persians to resupply horses locally. This limited the ammount of cavalry that could be deployed in Greece, and made what cavalry was deployed very vulnerable to attrition. In the second invasion, the Persians didn't actually suffer a land defeat until well after their fleet had been beaten and the Shahanshah had left. At that point, they'd lost the capacity to bring significant ammounts of supplies or reinforcements from Asia (even assuming Xerxes had them and was willing to run the bill up even higher on what was probably the most costly operation of Achaemenid history).

The Persian military system relied heavily on cavalry; the role of the Sparabara was to form a shield wall, which was effective against opposing archers and allowed them to hold off less disciplined troops, but they weren't meant to go toe to toe with heavy infantry or hold off shock cavalry. The best defence of both sparabara and archers against enemy cavalry was the Persian cavalry's superiority. Looking through the known equipment lists of the Persian cavalry, we see maces coming up—in EB terms, AP weapons making them heavy infantry killers. Add in their bows which would have enabled the cavalry to manoeuvre and shoot the vulnerable flanks and rear of a phalanx. Alexander removed that superiority of cavalry when he came along with his even heavier cavalry, at a time when the social class providing the core of the Achaemenid cavalry was in crisis.

I wouldn't say the Persian "Immortals" were inferior to the Greek/Macedonian heavy infantry. Certainly, the Greeks/Macedonians did not make that claim. However, the "Immortals" were an elite unit, a small part of the Persian armies, whereas almost all of Hellenic armies were capable of slugging it out in a prolonged melee. Even when/if the Persian elites defeated the units in front of them, they couldn't be everywhere and the battle could still be lost—indeed, frequently was (c.f. Mardonios and his guards making a last stand while their army routed).

In Alexander's campaigns, the peltastai would have played an important role against archery as well—with shields and some body armour, open order infantry could have drawn considerable ammounts of arrows and still taken very light casualties.