Moves Ash and Dawn Developed Together
One of the main characteristics of Pearlshipping is the way Ash and Dawn worked together, especially in the DP series, to improve each other's skills as trainers. "But this isn't romantic!" I hear you cry!
It's not romantic, but it's important. Now, we all know that the XY series has a more heavy focus on romance and blushing/jealousy than any other series, even the Original series with Misty's somewhat obvious display of attraction and jealousy in terms of Ash. But, we know in Pokemon, that the heaviest implication is still on becoming as good a trainer as possible, and it's pretty obvious that Dawn has contributed the most to Ash in terms of his skills as a trainer.
1. Firstly, one of the moves Ash and Dawn developed together was the Spin Dodge. This was first seen in DP017, Wild in the Streets, where Dawn uses Buneary and Piplup to save Ash and Pikachu from a hyperbeam.
Not only does Ash invite Dawn to train with him, he goes on to use the Spin Dodge in his Gym Battle against Roark.(Dawn also cheers for Ash in her cheerleader outfit in the episode, DP018, but that is beside the point) Ash also uses the Spin Dodge numerous times in his Sinnoh Battles.
2. Another move Ash and Dawn developed together was the Countershield. It even has its own Bulbapedia page here. Ash takes inspiration in developing this move after watching Dawn's Contest battle with Lila in DP095. It's an obvious example of how Ash and Dawn combined can produce a wonderful result. The Countershield is used time and time again. Ash uses it against Fantina, against Paul in the Sinnoh League, and it's even used in the BW series, with Dawn using it in her Evaluation battle with Cilan, much to Ash's delight.
3. This next move is one that Dawn explicity acknowledges that she and Ash developed together. Dawn first attempts the Ice Aqua Jet in DP041, but it doesn't work perfectly. However, Ash refines it and uses the move in DP078 in the Wallace Cup, and Brock tells May that Dawn was the one who invented it, while Dawn says that it was Ash's touch that made it work.
Ice Aqua Jet is used again in DP126 and and DP187 against Paul for the latter. This really reinforces how Ash and Dawn as a team is quite central to the DP series.
4. This "move" doesn't really have a name, but it's the move where Ash and Dawn's respective powerhouse Pokemon swallow their moves. Grotle swallows energyball and Mamoswine swallows iceshard. It arises when Grotle accidentally swallows his Energyball against Palmer (correct me if that's not true), and Dawn takes inspiration from this and uses this "power up" move in her contests.
Even from an objective point of view, it has to be said the Dawn has contributed to some degree to Ash's skills as a trainer, and from a Pearlshipper's point of view, I have to say that I think Dawn contributed THE MOST to Ash's skill as a trainer, out of all the Pokegirls. We'll have to wait and see what Serena does through the XY series. However, it will be very hard to top what Dawn did for Ash.
Please say in the comments if I've missed out any moves!