The relationship of Ash and Dawn can be explained by the relationship of their Pokemon, particularly Pikachu, Piplup, and Buneary. Ash and Dawn's Pokemon are a resemblance to the bond that they have with each other. And although this is true for many Ash pairings, the Pokemon involved between Ash and Dawn support its Ash ship the most.

Pikachu and Piplup:
Pikachu and Piplup represent the most important and prevalent point of Ash and Dawn's relationship: their friendship. These two Pokemon high five just like their trainers, walk together during journeys, and are the go-to Pokemon for Ash and Dawn. Both also have an unbreakable bond with their trainers even from the start when they warded off groups of Spearow and Ariados. Now Pikachu and Piplup have a very close friendship and they are Ash and Dawn's main Pokemon. This means that the main part of Ash and Dawn's relationship is their inseparable friendship.

Pikachu and Buneary:
Pikachu and Buneary represent a less significant but still an existing part of Ash and Dawn's relationship: their romance. Pearlshipping lacks in romantic moments, but keep in mind that it's their friendship that is of foremost importance. Buneary is Dawn's second Pokemon, so the romance between Ash and Dawn plays more of a minor role.

Quilava and Quilava:
Quilava and Quilava represent Ash and Dawn's equality. Both started off as Cyndaquil and were the 'babies' of the group. They went on to compete in gym battles and contests in their debut seasons. And when they evolved, they both used Eruption. The point of this is to show that Ash and Dawn are on equal level for each other and with each other since they have the same Pokemon. There are plentiful examples of their equality and the song 'High Touch' is probably the greatest. Advanceshipping, which is not mutually equal, is represented by Munchlax/Snorlax, Squirtle/Wartortle, and Bulbasaur/Venusaur; these are all unequal despite having evolutionary pairs. Ash and Dawn's Quilavas resemble something not found in any other Ash ship: Ash and Dawn being on the same level for one another.

Aipom and Buizel:
Aipom and Buizel represent Ash and Dawn's trust and their mutual cooperation. This is because Ash and Dawn trusted each other enough to trade in order to make their Pokemon even stronger.

Piloswine and Grotle:
In 'Get Your Rotom Running', both Piloswine and Grotle (who are both evolved now) playfully tackled their trainers out of love. Once again, this shows Ash and Dawn's equality but also their similar hearts for Pokemon.

Honorable Mentions:
Primeape and Ambipom:
-Primate Pokemon both left for training in Kanto
Luvdisc:
-Though not owned by Ash and Dawn, they both see Luvdisc, symbolizing Ash and Dawn's eternal love based on the Pokedex entry. Moreover, Pikachu and Buneary see the Luvdisc with them; remember Pikachu and Buneary represent Ash and Dawn's love.

Dawn's Cameo:

Oshawott played a big Pokemon role here. This Pokemon represents BW Ash, or Ash in the Best Wishes season.

Oshawott and Piplup:
These two both fell for Meloetta and hated each other for it. How is this related to Ash and Dawn? Iris and Cilan did take some the attention away from Ash and Dawn. Ash didn't like this since he wanted to battle Dawn first, but yet Ash and Dawn (and their two water Pokemon) still work as a pair throughout. The love-hate feelings between Piplup and Oshawott symbolize the underlying feelings of Dawn and Ash (but Ash in particular) that could have possibly been going on.

But when Dawn leaves, Piplup and Oshawott throw away every bit of jealousy/hate they had for each other and hug each other in tears. This represents that Ash and Dawn are still together and that above everything else they deeply care for each other.

Oshawott and Buneary:
Oshawott immediately fell in love with Buneary at first sight. At this point, both Pokemon are caught and Prof. Oak's theory can apply. If Oshawott = BW Ash and Buneary = the Pearlshipping romance, then this shows that Ash's love is still existent.

Ash desired to battle Dawn when she came back, but Cilan stepped in, making Ash disappointed. Also, Ash didn't care when Iris called him a kid, but was disappointed when Dawn agreed. Oshawott's exterior relations with Piplup and Buneary resemble how Ash feels in BW.

And Buneary only rejects Oshawott to go to Pikachu in that episode. Just as the love Between Pikachu and Buneary lasted, Ash and Dawn's relationship lasted as well.

Ash and Dawn may not always externalize their bond. The Pokemon can do it for them.