The singer just filed legal docs asking for a dissolution of marriage from his wife, Jae Lin ... to whom he's been hitched for a long time. In fact, contrary to the year the public seems to have thought they tied the knot (2011) ... AP cites 2010 as the year they got married.

Now, as far as their separation date ... it doesn't sound like Anderson even knows when that was -- 'cause he leaves it blank here in the paperwork, and simply writes "TBD."

Still, he makes no bones about the fact that he wants a straight-up divorce -- as opposed to a legal separation -- and goes on to list their two minor children as individuals they'll need to hash out custody over ... and right off the bat, he seems willing to share parenting duties.

Anderson notes in his filing that he wants himself and Jae to have joint legal and physical custody of their kids ... with a visitation schedule for both of them. In terms of divvying up their assets/property ... AP says he and his legal team still need to ascertain who owns what.

Like we said, they've been a couple for a while now -- and Anderson's pretty low-key about his private life ... even though, professionally, he's been skyrocketing over the past few years.