Characteristics of rogue waves on a periodic background for the Hirota equation

We consider the rogue dn-periodic waves (the rogue wave solutions on the dn-periodic waves background) for the Hirota equation by using Darboux transformation. We take Jacobian elliptic function do as a seed solution, which is modulationally unstable as regards long wave perturbations. Through nonlinearization of the Lax pair for Hirota equation, the corresponding periodic eigenfunctions are successfully obtained. Based on these periodic eigenfunctions, we further construct the solutions of the Lax pair equations with dn-periodic wave seed solutions. In addition, numerical simulations are presented to reveal the phenomena of these solutions under different parameters choices. (C) 2019 Elsevier B.V. All rights reserved.