Multi-rogue waves and rational solutions of the coupled nonlinear Schrödinger equations

In this paper, the modified Darboux transformation method is applied to the coupled nonlinear Schrödinger (CNLS) equations. By using the iterative algorithm of the Darboux transformation, the multi-rogue wave solutions of CNLS equations are generated from the plane wave solution. The hierarchies of first-, second- and third-order rational solutions with free parameters are explicitly presented. Some basic properties of multi-rogue waves and their collision structures are studied on the basis of the solutions obtained. In addition, the relation of rational solutions between NN-CNLS equations and CNLS equations is explained. Our results might provide useful information for investigating the dynamics of multi-rogue waves in the deep ocean and nonlinear optical fibers.