Can also be translated to peter doesnt need to sleep or peter doesnt want to sleep. As with all modal verbs, it can mean have to or need to or want to.
Peter doesn't need to sleep (peter ko soney ka jarurath nahi hai)
Peter doesn't want to sleep (Peter sona nahi chahta hai)
Generally you can have just नहीं instead of नहीं है in negative sentences. I'm not sure how common it is in real spoken/written Hindi.