Generalized Darboux transformation and high-order solutions for the modified complex short pulse equation

We construct the generalized Darboux transformation for the modified complex short pulse (mcSP) equation. As applications, we present high-order solutions for the mcSP equation by the generalized Darboux transformation. In the case of zero seed solution, high-order soliton solutions are derived, and in the case of plane wave seed solution, high-order rogue wave solutions are obtained. As examples, some high-order solutions and their dynamics are illustrated graphically.