Adam Clarke on Psalms 137:1

By the rivers of Babylon - These might have been the Tigris and Euphrates, or their branches, or streams that flowed into them. In their captivity and dispersion, it was customary for the Jews to hold their religious meetings on the banks of rivers. Mention is made of this Act 16:13, where we find the Jews of Philippi resorting to a river side, where prayer was wont to be made. And sometimes they built their synagogues here, when they were expelled from the cities.