Course of the War
The war began when Persian invaders first advanced on northern Egyptian provinces. They made good progress against the Egyptians, until they met them at the Belusium. However, prior to the beginning of the battle, an unexpected sandstorm picked up, scattering the Persian armies.
Battle of Belusium
With the Persian forces broken, and scattered, the Egyptian armies, lead by Psamtik III, attacked the Persians. Still broken, and lacking proper cohesion, the Persian forces were repelled, and defeated by the Egyptians. The Persians reatread, but the Egyptians took signficiant casualties, and did not pursue them.
The defeat of the Persians proved a major turning point in the war. Greek forces, impressed by the Egyptian skill, decided to stand with the Egyptians. A combined Greek, Egyptian attack force attacked the Persians at Yamit, and crushed them decisively.
The defeat at Yamit proved to be the crushing blow for the Persian invasion. The Persian forces were forced to retreat, and Cambyses agreed to sign a treaty with the Egyptians, establishing the borders between the two Empires.
The Egyptian victory during the Persian-Egytpain War was the pivotal event in the timeline, being one of the driving forces in Egypt's developing. Hoping to restrengthen his empire, Psamtik, and his successors would expand to the South, opposed to the North, not interested in pursuing conflict anytime soon with the Persians. This lead to Egyptian expansion in the South for the next couple generations.