Periodic travelling waves and rogue waves for the higher-order modified Korteweg-de Vries equation

摘要

In this paper, we construct the rogue wave solutions of the higher-order modified Korteweg-de Vries equation on the background of the general periodic travelling wave so-lutions. By the sub-equation method, we derive the general periodic travelling wave solu-tions expressed in terms of the Jacobi elliptic functions. By using the Darboux transforma-tion method, we derive one-, two-, and three-fold rogue wave solutions on the background of elliptic functions. We provide some examples of two families of rogue wave solutions for illustration. The method provided in this paper can also be applicable to the construction of rogue wave solutions of other higher-order nonlinear integrable models on the periodic wave background.(c) 2021 Elsevier B.V. All rights reserved.