The notion that the Rhine remained the border has been superseded by evidence. There's an anachronistic nationalistic urge that really picked up steam in the mid 19th century, in Germany, Scotland, Britain, France, etc to invent "resistance" to "occupation" but it's merely quaint now. When Diocletian re-established a unified empire, he nevertheless split it into four parts, and the western/northern area had its capital in what's now Trier. The city of Cologne got its name from "Colonia Claudia Ara Agrippinensium". Traces of Roman camps and such have been id'ed a good bit farther east in recent years.