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

Rogue waves (RWs) are unexpectedly strong excitations emerging from an\notherwise tranquil background. The nonlinear Schr\\"odinger equation (NLSE), a\nubiquitous model with wide applications to fluid mechanics, optics and plasmas,\nexhibits RWs only in the regime of modulation instability (MI) of the\nbackground. For system of multiple waveguides, the governing coupled NLSEs can\nproduce regimes of MI and RWs, even if each component has dispersion and cubic\nnonlinearity of opposite signs. A similar effect will be demonstrated for a\nsystem of coupled derivative NLSEs (DNLSEs), where the special feature is the\nnonlinear self-steepening of narrow pulses. More precisely, these additional\nregimes of MI and RWs for coupled DNLSEs will depend on the mismatch in group\nvelocities between the components, as well as the parameters for cubic\nnonlinearity and self-steepening. RWs considered in this work differ from those\nof the NLSEs in terms of the amplification ratio and criteria of existence.\nApplications to optics and plasma physics are discussed.\n