Threads of Time

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 …