Soundproofing is the best way out but just out of curiosity, do they live so close by? They are neighbors who will always start trouble irrespective of whether or not there is a genuine reason to do so.
Based on what ABtoJayZ, the house they are living in is a duplex, meaning it is a house divided in two. Sounds travel faster through solids, so it is no surprise if the neighbors will complain because the barrier won't block the sound.