  It was conjectured by Witten that a BPS-saturated domain wall exists in the
M-theory fivebrane version of QCD (MQCD) and can be represented as a
supersymmetric three-cycle in the sense of Becker et al with an appropriate
asymptotic behavior. We derive the differential equation which defines an
associative cycle in $G_2$ holonomy seven-manifold corresponding to the
supersymmetric three-cycle and show that it contains a sum of the Poisson
brackets. We study solutions of the differential equation with prescribed
asymptotic behavior.
