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Rogue waves (RWs) are unexpectedly strong excitations emerging from anotherwise tranquil background. The nonlinear Schr\"odinger equation (NLSE), aubiquitous model with wide applications to fluid mechanics, optics and plasmas,exhibits RWs only in the regime of modulation instability (MI) of thebackground. For system of multiple waveguides, the governing coupled NLSEs canproduce regimes of MI and RWs, even if each component has dispersion and cubicnonlinearity of opposite signs. A similar effect will be demonstrated for asystem of coupled derivative NLSEs (DNLSEs), where the special feature is thenonlinear self-steepening of narrow pulses. More precisely, these additionalregimes of MI and RWs for coupled DNLSEs will depend on the mismatch in groupvelocities between the components, as well as the parameters for cubicnonlinearity and self-steepening. RWs considered in this work differ from thoseof the NLSEs in terms of the amplification ratio and criteria of existence.Applications to optics and plasma physics are discussed.

Rogue waves for a system of coupled derivative nonlinear Schr\"odinger equations