Rogue periodic waves in the fifth-order Ito equation

Abstract In this letter, with the nonlinearization of spectral problem (NSP) and the Darboux transformation method, we construct rogue wave solutions of the fifth-order Ito equation on the elliptic function background. Considering the NSP of the Ito equation, we obtain admissible eigenvalues and the corresponding periodic and non-periodic eigenfunctions of spectral problem. By the one-fold and two-fold Darboux transformations, we respectively present rogue waves on the background of the Jacobi elliptic dn and cn functions.