In the new form i am populating the current user as a default value like that how to populate the current user in the edit form as well
I've just tested this with Nintex Forms 2013 (v22.214.171.124) and if you set the default value and save the item, when you open the item to edit, the value was saved with the item.
Are you not seeing this? If not, I'd recommend you upgrade Nintex Forms to the latest version.
Also, are you able to reproduce this with a simple form and then export and share it here?
when i create a item it taking the default value as my name but in the edit item when other person is editing the item it has to display his the name of the current username .Is any script i have to use for this.
SPServices on codeplex: jQuery Library for SharePoint Web Services - Home
SPServices Documentation for SPGetCurrentUser: jQuery Library for SharePoint Web Services - Documentation