Abstract
The coupled derivative nonlinear Schrödinger III (cDNLSIII) equation describes pulse propagations in a two-mode nonlinear fiber. In this paper, we construct the N-fold generalized Darboux transformation (DT) with the limit approach, from which the general higher-order rogue wave solutions of the cDNLSIII equation are obtained. These solutions, divided into three categories, namely, rogue waves and rogue waves on multi-soliton and multi-breather backgrounds, have applications in nonlinear fiber communication. Furthermore, we present some interesting interactions between rogue waves and solitons or breathers and analyze the features of each type.
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