The following article contains an answer for the question: What is the name of the person who brought in people on ships, who engaged in a sea-fight there, impersonating the Corcyreans and Corinthians? , can you please find it? 

Dio, Suetonius and Martial all record naumachiae, the commonly used Greek term for what the Romans also called navalia proelia, re-creations of famous sea battles. While Dio claims that both the purpose-built naumachia of Augustus and the amphitheatre itself were flooded for two separate shows, Suetonius states only that the event took place on the old artificial lake (which would have been that of Augustus). Martial does not specify where the naumachiae took place, but he is clear that whatever location he is discussing could be flooded and drained at will:
If you are here from a distant land, a late spectator for whom this was the first day of the sacred show, let not the naval warfare deceive you with its ships, and the water like to a sea: here but lately was land. Don't you believe it? Watch while the waters weary Mars. But a short while hence you will be saying "But here lately was sea."
It appears it would have been difficult to flood the amphitheatre, but, because few records survive on the operation of the Colosseum, it is impossible to say for certain where the naval battles took place. Suetonius writes that Titus' brother and successor, Domitian, staged sea-fights in the amphitheatre, but he had made alterations to the structure, which probably included adding the hypogeum—a complex of underground passages that may have allowed the arena to be quickly flooded and emptied. While Suetonius only records that Titus' recreations of naval battles took place, Dio gives some details:
For Titus suddenly filled this same theatre with water and brought in horses and bulls and some other domesticated animals that had been taught to behave in the liquid element just as on land. He also brought in people on ships, who engaged in a sea-fight there, impersonating the Corcyreans and Corinthians; and others gave a similar exhibition outside the city in the grove of Gaius and Lucius, a place which Augustus had once excavated for this very purpose.

Titus