Strong coupling of Schrödinger equations: Conservative scheme approach Original Research Article

The system of coupled nonlinear Schrödinger’s equations (CNLSE) is considered and the physical meaning of the coupling terms is identified. The attention is focused on the case of real-valued parameter of linear cross-diffusion. A new analytical solution for the coupled case is found and used as initial condition for the interaction and evolution of two pulses. Conservative numerical scheme and algorithm are devised for the time evolution of solitons in CNLSE. The results show that the coupling term brings into play localized solutions with rotating polarization which in many instances behave as breathers. Both elastic and inelastic collisions are uncovered numerically.