From Tokyopop:

High-school student Moon Bin Lee has difficulty sleeping due to a recurring nightmare: he's stranded over a thousand years in the past chasing a dark-haired girl into a deep abyss.

Before long, the nightmare overwhelms him, and he is unable to tell whether he is Moon Bin, a Seoul teenager at the end of the second Millennium, or Sa Kyoung Kim, the son of a prominent warrior family in the middle of the first Millennium. People in his present-day life assume roles in his historical life as he struggles to learn exactly who he is and what he's expected to do, straddling a transmigratory portal through time and space.

In the present, his school's kendo club battles to stay in the championships... but in the past, Moon Bin finds himself at the threshold of a territorial dispute on the plains of Mongolia.