Vector soliton pairs for a coupled nonautonomous NLS model with partially nonlocal coupled nonlinearities under the external potentials

A (3+1)-dimensional coupled nonautonomous NLS model with partially nonlocal coupled nonlinearities under the linear and harmonic potentials becomes the center of attention. Two kinds of the reductions from the nonautonomous coupled NLS model to autonomous (2+1)-dimensional and (1+1)-dimensional NLS models are erected, respectively, and the comparison of two reductions is performed and analyzed. Based on solutions of autonomous (2+1)-dimensional and (1+1)-dimensional NLS models, via the Hirota and Darboux methods, two kinds of vector nonautonomous soliton pairs with localized and non-localized structures in three-dimensional space are constructed. Evolutional behaviors of these vector solitons are explored in the periodical system.