Dressing method for the multicomponent short-pulse equation

We use the Zakharov–Shabat dressing method to solve the multicomponent short-pulse equation. We obtain dressed solutions of this equation using a Riemann–Hilbert problem. The dressed solutions of the Lax pair and the multicomponent short-pulse equation are expressed in terms of Hermitian projectors. We show that the dressed solutions are related to quasideterminant solutions, and we write $K$-soliton solutions in terms of quasideterminants. In explicit form, we obtain one- and two-soliton solutions.