An Epithet of the River Styx

I have a question that falls under literature, but I remember that Dante, Greek mythology, and Milton were required reading in my English courses in high school and university.

It's about an epithet that was, I think, made popular only by the book series Percy Jackson and the Olympians by Rick Riordan. In the series, the River Styx has been described and portrayed as the "River of Lost Dreams and Hopes." This, it would seem, has been picked up and applied by some people on the Net. But I can't find any other case when the Styx was previously described as such.

Of course I imagine the Styx must be a very barren and desolate place but, still, I would like to check if there are any other lines from perhaps Dante or another writer that could've inspired such a title. Or is it one writer's completely fresh and unique version, an employment of his artistic license?

Solution 1:

Book VI of Virgil’s ‘Aeneid’ describes the descent of Aeneas into the underworld, to reach which he must cross the river Styx. I’ve had a quick look at Dryden’s verse translation, but can’t find the actual description of the Styx that you quote. You may like to have a closer look yourself, if you have the time. (If you read Latin, the original is here.)

Solution 2:

Even before Virgil, Hesiod described the Styx as one of the rivers of the Underworld. It's never easy in Greek mythology to distinguish the characteristics of the actual river (which was supposed to be corrosive, though it certainly isn't these days), the character of the river-nymph and the wider characteristics conventionally attributed to a stream supposed to flow out of the Underworld ; but it is intersting that the Greek for hatred is stygos.