Palkia and Dialga represent two of the creation trio in Pokemon, introduced to Generation IV of the series.
Pokemon Diamond and Pearl were revolutionary. Those games were followed by Pokemon Platinum, continuing the trend of a third game in the Generation at the time.
Both of these Legendaries were originally only found in the title they graced the cover of. However, when Platinum came around, both Pokemon were available in that game for players to capture.
How to catch Palkia and Dialga in Pokemon Platinum
Palkia and Dialga can be caught in Pokemon Platinum after defeating the Elite Four. In Mt. Coronet, there will be two items to pick up. Be sure to have HM Waterfall available for use.
Atop the waterfall, hidden in a cave, are the Adamant and Lustrous Orbs.
Head to Celestic town and meet Cynthia there. You will be able to speak with her grandmother. Cynthia's grandmother will read a story about the Legendary Pokemon after you show her the two Orbs obtained from Mt. Coronet.
Go to the ruins in Celestic town and interact with the painting inside. Cynthia will appear again. She will speak about Palkia, Dialga, and Giratina. Once these tasks have been completed, the Legendary Pokemon encounters become available.
The peak of Mt. Coronet is the Spear Pillar. This is where the two Legendary Pokemon can be battled. There will be a blue portal there. Interact with it, and then you will be able to battle Dialga. Exit the area and return immediately. A pink portal will now appear. Interacting with this portal will initiate the encounter with Palkia.
Be sure to save before both battles and purchase plenty of Ultra Balls. These two Legendary Pokemon are no pushovers. It might take some time, especially if you don't have a Master Ball for one of them.