  We propose new type of discrete and ultradiscrete soliton equations, which
admit extended soliton solution called periodic phase soliton solution. The
discrete equation is derived from the discrete DKP equation and the
ultradiscrete one is obtained by applying the ultradiscrete limit. The soliton
solutions have internal freedom and change their shape periodically during
propagation. In particular, the ultradiscrete solution reduces into the
solution to the ultradiscrete hungry Lotka-Volterra equation in a special case.
