The classical solutions with $k_{-}=0$ in Kaku theory

We consider Kaku theory as introduced in M. Kaku, Phys. Lett. B 200, 22 (1988) and investigate classical solutions. In particular, we obtain that the equation of motion with the restriction $k_{-}=0$ in the Kaku theory is equivalent to the equation of motion in Witten theory. Because of this property, some solutions including the tachyon vacuum solution in the Witten theory satisfy also the equation of motion in the Kaku theory. In addition, we confirm that the cohomology around the tachyon vacuum solution is trivial also in the Kaku theory.