I have seen similar situations any number of times. In every single case, the man made having a new woman in his life a central and immediate issue, in order to demonstrate to his ex that he was still desirable, sexy, interesting etc. and make her aware of what she had lost/thrown away when they parted company. In my opinion, such behaviour, while still loutish, is understandable in an adolescent who has just busted up with his first great love. In the case of an adult, it is simply pathetic.
Of course, this may not be the case with your ex, especially as you say your parting was a mutual decision. Of course, that can still result in emotional turmoil, feelings of rejection, fears about growing old, resentment, desire for revenge and all sorts of other nasty and destructive emotions.
Looking great and being charming to the new woman is often and effective response.