I have horizontal neck bands since I was a baby, and quite pronounced muscles underneath my neck. (photo)

From the photo it looks like you don't have significant sun damage, which is great.  Although you would need to be evaluated during movement and at rest, it appears that the lines could be improved with a combination of hyaluronic acid gel filler and botulinum toxin.  I would use a microcannula to place a thin filler, like Belotero, superficially within the wrinkles themselves.  Belotero is nice because it can be safely injected high in the skin to directly lift up an etched line or wrinkle.  At the same time, injecting the platysma muscle directly and then the surrounding area with dilute microdroplets with a botulinum toxin like Botox, Xeomin or Dysport, can soften the pull on the skin to relax the muscles and therefore the lines.  Doing both gives a better and longer lasting result than either alone.  I do recommend starting the toxin gradually to avoid weakening the area too much.

Deep horizontal neck bands are difficult problem to treat, especially in a young person. Options include Botox injection, fat grafting or dermal fillers in conjunction with Botox or surgical release combined with repeat fat grafting under the skin ...Consult a facial plastic surgeon for this problem.