I bought the Jupiter soprano trombone.
I am a pianist and have studied acoustics so I think I can find my way on the instrument.
Since this instrument is kind of a trombone/trumpet hybrid, I got books for trumpet and trombone by Arban.
But, as I started studying I figured out that nothing applies on the soprano.
How should I study?

Get a book specifically for the soprano trombone

Are there any? I can't find one..

You should be able to use just the trumpet Arbans, since your instrument is (kinda) essentially a slide trumpet. Both instruments have the same range, and the slide positions tranfser perfectly to trumpet fingerings.

You will just need to find a sop bone slide chart...