It is good you have decided not to chase after her. It would be futile for you would be hurting yourself in the long run. Her breaking up with you is for your own good even though it hurts.
Erasing her memory from your mind in an instant is not possible. However, if you want to heal and recover from the relationship you have to be determined and disciplined.
First, delete her numbers from your phone and block her on your social media accounts. This will prevent you from giving in to the urge to want to send her text or look at her posts or photos.
Secondly, tear apart and burn her photos. They are no longer of any use to you. They will always remind you of her. This includes any possession of hers that you have. You can decide to return them to her, store away or get rid of them.
Engage in activities that will keep you from thinking about her. You shouldn't be busy, but activities such as hobbies do help a lot.
Don't listen to sad songs and when you begin thinking about her, snap out of it. Always tell yourself she is no longer yours. Stop as soon as possible replaying the good times you shared or thinking about the relationship.
Don't hate or hold a grudge against her anymore. Don't hate her and forgive her.
I have written articles on how to heal and recover from a relationship and things you should never do after a breakup.