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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.
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.