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

Hui Mao, Xue Zhang, Fengdie He

School of Mathematics and Statistics, Nanning Normal University, Nanning, Guangxi, China

Abstract: 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.

Keywords: modified complex short pulse equation, generalized Darboux transformation, high order soliton solutions, high order rogue wave solutions.

MSC: 37K10;35Q51

Received: 25.02.2025
Revised: 03.04.2025

DOI: 10.4213/tmf10960

 English version: Theoretical and Mathematical Physics, 2025, 225:1, 1844–1858

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