Rogue waves on the periodic background in the higher-order modified Korteweg-de Vries equation

摘要

In this paper, we investigate the higher-order modified Korteweg-de Vries (mKdV) equation by using an algebraic method. On the background of the Jacobi elliptic function, we obtain the admissible eigenvalues and the corresponding non-periodic eigenfunctions of the spectral problem in this higher-order model. Then, with the aid of the Darboux transformation (DT), we derive the rogue dn- and cn-periodic wave solutions. Finally, we analyze the non-linear dynamics of two kinds of rogue periodic waves.