Abstract
In this paper, rogue wave solutions of the higher-order dispersive nonlinear Schrödinger equation are investigated, which describe the propagation of ultrashort optical pulse in optical fibers. The Nth-order rogue wave solutions with 2N + 1 free complex parameters are constructed via the generalized Darboux transformation method. As applications, rogue waves from the first to the fifth order are calculated according to different combinations of parameters. In particular, rogue waves dynamics and several new spatial–temporal structures are also discussed and exhibited to make a comparison with those of the nonlinear Schrödinger equation.
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