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The dynamics of a one-dimensional, highly discrete, linear array ofalternating $0-$ and $\pi-$ Josephson junctions is studied numerically, underconstant bias current at zero magnetic field. The calculated current - voltagecharacteristics exhibit half-integer and integer zero-field-like steps for evenand odd total number of junctions, respectively. Inspection of theinstantaneous phases reveals that, in the former case, single $\pi-$kinkexcitations (discrete semi-fluxons) are supported, whose propagation in thearray gives rise to the $1/2-$step, while in the latter case, a pair of$\pi-$kink -- $\pi-$antikink appears, whose propagation gives rise to the$1-$step. When additional $2\pi-$kinks are inserted in the array, they aresubjected to fractionalization, transforming themselves into two closely spaced$\pi-$kinks. As they propagate in the array along with the single $\pi-$kink orthe $\pi-$kink - $\pi-$antikink pair, they give rise to higher half-integer orinteger zero-field-like steps, respectively.

Mobile $\pi-$kinks and half-integer zero-field-like steps in highly discrete alternating $0-\pi$ Josephson junction arrays