The evolution of periodic waves of the coupled nonlinear Schrödinger equations Original Research Article

Systems of coupled nonlinear Schrödinger equations (CNLS) arise in several branches of physics, e.g., hydrodynamics and nonlinear optics. The Hopscotch method is applied to solve CNLS numerically. The algorithm is basically a finite difference method but with a special procedure for marching forward in time. The accuracy of the scheme is ensured as the system is proved to satisfy certain conserved quantities. Physically, the goal is to study the effects of an initial phase difference on the evolution of periodic, plane waves. The outcome will depend on the precise nature of the cubic nonlinearity, or in physical terms, the nature of polarization in optical applications.