And pardon me but who's Ayame?
Ayame is a character that doesn't appear in the Inu Yasha manga, she's Anime only.
Shes a female wolf youkai who claims to be Kouga's fiancee. Ayame's grandfather is the leader of the Mountain Wolf's of the north. When they where younger, Kouga jokingly promised to marry Ayame. She, however, took it seriously. Kouga claims to not remember. However, a flashback later on reveals that he does, indeed, remember. He saved Ayame from the Birds of Paradise. He lied to her because he says his mission is to destroy Naraku (Which he believes will lead to his inevitable death), and wishes for her to forget him.
In an entirely obvious twist, at the end of it all, they show her saying she will never forget him, LOL.
I.....don't get out much.....
Sadly, this is really one of the few times the anime related information I spend time memorizing comes in handy.
Actually, its the only time, but, lets not get into how sad that really is.