Multisolitons, breathers, and rogue waves for the Hirota equation generated by the Darboux transformation.

The determinant representation of the n-fold Darboux transformation of the Hirota equation is given. Based on our analysis, the 1-soliton, 2-soliton, and breathers solutions are given explicitly. Further, the first order rogue wave solutions are given by a Taylor expansion of the breather solutions. In particular, the explicit formula of the rogue wave has several parameters, which is more general than earlier reported results and thus provides a systematic way to tune experimentally the rogue waves by choosing different values for them.