Rogue waves of the coupled modified nonlinear Schrödinger equations

Abstract

In this paper, we employ the generalized Darboux transformation to obtain rogue wave solutions of the coupled modified nonlinear Schrödinger equations. By considering both double-root and triple-root situations of the spectral characteristic equation, we derive the first-order and second-order rogue wave solutions. We find that this coupled system admits abundant spatiotemporal patterns of rogue waves including the double, triple, quadruple and sextuple structures. In addition, we also demonstrate the coexistence dynamics of rogue waves, which depend on the choice of structural parameters.