Darboux transformation for a semidiscrete short-pulse equation

We define a Darboux transformation in terms of a quasideterminant Darboux matrix on the solutions of a semidiscrete short-pulse equation. We also give a quasideterminant formula for $N$-loop soliton solutions and obtain a general expression for the multiloop solution expressed in terms of quasideterminants. Using quasideterminants properties, we find explicit solutions and as an example compute one- and two-loop soliton solutions in explicit form.