When American born, bred, raised, etc. singer-songwriter Edward Joseph Mahoney sings
I've got two tickets to paradise (youtube link)
(Compare: I've got two tickets in my pocket)
I possess two tickets to paradise
I have acquired two tickets to paradise
which in AmE would usually be expressed as
I've gotten two tickets to paradise. (AmE present perfect)
whereas in BrE it would usually be expressed as
I've got two tickets to paradise. (BrE present perfect and 'double form of have')
Typical BrE usage of I've got as present perfect:
I've got Pippet a new jumper, think she'll like it?
(In AmE, we would say I've gotten Pippet a new sweater.)
Now you should know that I've got can mean I possess in both BrE and AmE.
The Beatles provide an example of BrE in I've got a feeling, while another two of many many American uses are those of Frank Sinatra in I've got you under my skin and Garth Brook's (I've got) friends in low places (1:13 etc).
Note that in both BrE and AmE, I've got can also express obligation, as in
I've got to clean my room before I can go to the concert.