  The existence of K-instantons on a cylinder M^7 = R_tau x K/H over a
homogeneous nearly K"ahler 6-manifold K/H requires a conformally parallel or a
cocalibrated G_2-structure on M^7. The generalized anti-self-duality on M^7
implies a Chern-Simons flow on K/H which runs between instantons on the coset.
For K-equivariant connections, the torsionful Yang-Mills equation reduces to a
particular quartic dynamics for a Newtonian particle on C. When the torsion
corresponds to one of the G_2-structures, this dynamics follows from a gradient
or hamiltonian flow equation, respectively. We present the analytic (kink-type)
solutions and plot numerical non-BPS solutions for general torsion values
interpolating between the instantonic ones.
