Vector solitons in an extended coupled Schrödinger equations with modulated nonlinearities

We developed a method to investigate the vector solitons in an extended non-autonomous coupled Schrödinger equations with cubic and quintic nonlinearities in which the external potentials of the model depend in space and time, and all the remaining of its coefficients are time dependent. We mapped this system into an autonomous one under a specific set of constraint conditions on the variable coefficients of the model and then analyzed the regions with modulational instabilities. Front, bright and dark vector solitons associated with the original system are obtained. Some applications and a numerical simulation based on a Fourier split-step method are discussed.