Abstract
In this paper, higher-order localized waves for a coupled fourth-order nonlinear Schrodinger equation are investigated via a generalized Darboux transformation. The Nth-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.