Vector rogue waves in integrable M-coupled nonlinear Schrödinger equations

We consider a set of integrable M-coupled nonlinear Schrödinger (M-CNLS) equations, with arbitrary M arising in several physical contexts including nonlinear optics and atomic condensates. We employ the Kadomtsev–Petviashvili hierarchy reduction method for deriving the general vector rogue wave (RW) solution of the M-CNLS equations in a compact form. All orders of vector RWs can be written down from this general solution by fixing the parameters appropriately. Single, double, triple and quadruple vector RWs are obtained for focusing, defocusing and focusing–defocusing (mixed) M-CNLS systems. Especially, for the mixed M-CNLS system for the first time we report the RW doublet. In addition, we also identify several other intriguing multi-RW structures namely bright-dark composites, bright-dark triplets, bright-bright and bright-dark quartets. (paper)