Rogue wave solutions for the coupled cubic-quintic nonlinear Schrödinger equations in nonlinear optics

A generalized Darboux transformation for the coupled cubic-quintic nonlinear Schrödinger equation is constructed by the Darboux matrix method. As applications, the Nth-order rogue wave solutions of the coupled cubic-quintic nonlinear Schrödinger equation have been obtained. In particular, the dynamics of the general first- and second-order rogue waves are discussed and illustrated through some figures.