Higher-order localized wave solutions to a coupled fourth-order nonlinear Schrödinger equation

In this paper, higher-order localized waves for a coupled fourth-order nonlinear Schrödinger equation are investigated via a generalized Darboux transformation. The [Formula: see text]th-order localized wave solutions of this equation are derived via Lax pair and Darboux matrix. Evolution plots are made and dynamical characteristics of the obtained higher-order localized waves are analyzed through numerical simulation. It is observed that rogue waves coexist with dark–bright solitons and breathers. The presented results also show that different values of the involved parameters have diverse effects on the higher-order localized waves.