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I never experienced this but when my friend was broken up with, he was visibly depressed for about two weeks then slowly went to being upbeat like he usually was. I don't think that picture is an accurate depiction and more or less is determined by the person.
For me, this is true especially the month part because that phase extended well past one month for me, I am on my fourth month after the breakup from my first real relationship and I still feel like that sometimes. It did take a while to process the breakup for me because I felt like I was strong and could handle it, man oh man was I wrong. It was so bad right now that I am seeing a therapist because my self destructive behavior was ruining my life and I was trying to keep myself busy with other activities but it was as effective as a band-aid on a lost limb.