Rogue waves for the Hirota equation on the Jacobi elliptic cn-function background

In this paper, the exact rogue wave solutions for the Hirota equation are investigated on the Jacobi elliptic cn-function background. Under the Bargmann constraint, the differential constraints on the potential are obtained by the nonlinearization of spectral problem. Further, the eigenvalues are determined based on the differential constraint equations. The non-periodic solution of spectral problem is constructed, which can produce rogue periodic wave solutions of the Hirota equation. Moreover, the exact rogue periodic wave solutions are presented via the one- and two-fold Darboux transformation formulas. Finally, the generation mechanism and characteristics of rogue periodic waves are analyzed from the viewpoint of two- and three-dimensional structures.