Dynamics of the breathers and rogue waves in the higher-order nonlinear Schrödinger equation

In this paper, the higher-order nonlinear Schrödinger equation, which can be widely used to describe the dynamics of the ultrashort pulses in optical fibers, is under investigation. By means of the modified Darboux transformation, the hierarchies of breather wave and rogue wave solutions are generated from the trivial solution. Furthermore, the main characteristics of the breather and rogue waves are graphically discussed. The results show that the extreme behavior of the breather wave yields the rogue wave for the higher-order nonlinear Schrödinger equation.