Abstract
In this paper, the rational solutions with arbitrary constants of a Hirota equation are presented employing the Darboux transformations. Then, the similarity transformation allows us to relate certain class of multi-rogue wave solutions of the higher-order nonlinear Schrödinger equation (NLSE) to the solutions of (1+1)-dimensional integrable Hirota equation. The multi-rogue wave solutions with arbitrary constants are considered. The obtained rogue wave solutions can be used to describe the possible formation mechanisms for optical and Bose–Einstein condensates.
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