That carpet wave situation is the worst. Rented a carpet stretcher from the hardware store last year when my own install went sideways. Just a few bucks for the day and it pulled everything tight as a drum. You have to work from the center out towards the walls. Made a huge difference. Think your neighbor would ever try to fix it, or is it a permanent ocean view now?
My landlord in college had us fix a wave with a rented stretcher from Ace Hardware. It took two people, one to stretch and one to hold the edges down. If your neighbor ignores it, those waves just get BIGGER over time. Seriously, spending twenty bucks on a rental is way cheaper than replacing the whole carpet. Hope they listen to reason before it becomes a tripping hazard.
What about the padding underneath? If it's worn out or cheap, stretching the carpet won't last. Old foam padding breaks down and lets the carpet shift, so it'll just buckle again in a few months. You might need to replace the pad too, which adds cost but fixes it for good.