Rogue wave solutions for the generalized fifth-order nonlinear Schrödinger equation on the periodic background

Abstract

In this paper, we construct the rogue wave solutions on the background of the Jacobi elliptic functions for a generalized fifth-order nonlinear Schrödinger (NLS) equation. Using the Jacobi elliptic function expansion method, we reduce this higher-order nonlinear equation to a lower-order ordinary differential equation. Through the approach of the nonlinearization of spectral problem and then the Darboux transformation method, two kinds of rogue periodic waves which are on dn and cn Jacobi elliptic functions background are obtained. Furthermore, we represent the nonlinear dynamics of the rogue periodic wave solutions of this higher-order equation.