In order to obtain one of these legendary studies, you must complete a series of 7 Research Breakthrough by validating them once a day (only one stamp is valid per day).
Research Breakthrough can be collected in Pokéstop and it is then sufficient to successfully complete the mission requested by Professor Willow. After 7 successful quests, Professor Willow will randomly offer you one of the following Pokémon:
Articuno, Zapdos, Moltres, Kyogre & Groudon