Modulational instability and exact solutions for a three-component system of vector nonlinear Schrödinger equations

The modulational instability (MI) of the three-component system of vector nonlinear Schrödinger equations is investigated. It is found that there are a number of possibilities for the MI regions due to the generalized nonlinear dispersion relation, which relates the frequency and the wave number of modulating perturbations. Some classes of exact traveling wave solutions are obtained. Under some special parameter values, some representative wave structures are graphically displayed. These solutions are obtained by the use of F-expansion method.