First off, talk to Prof. Oak in Eterna City (he lives in the house in the southwest end next to the gym) and he will the three have been seen around Sinnoh. Track them with your Marking Map Poketch app. If Oak is not in his home, you may have to talk to him first in Pal Park, afterwards he will be in Eterna City.
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No,But You Can Get Moltres,Zapdos,And Articuno.
Articuno Zapdos Moltres
Yes, all 3 of them (Articuno, Zapdos and Moltres) will be in Pokémon HeartGold and Pokémon SoulSilver.
The catch rate for the three legendary birds is 3 in all of the games, including Platinum.
i would say zapdos moltres and articuno because they are all flying Pokemon and articuno is ice so it can have a chance of freezing the other ones.