Asymptotic behaviors of mixed-type vector double-pole solutions for the discrete coupled nonlinear Schrödinger system

In this paper, we analyze the asymptotic behaviors of mixed-type vector double-pole solutions for the discrete coupled nonlinear Schrödinger system with the focusing-focusing or focusing-defocusing nonlinearities applied in optical waveguide arrays. First of all, based on the bright-bright and bright-dark vector two-soliton solutions given by the Hirota method, we construct the mixed-type vector double-pole solutions via the limit technique. Then, through a modified asymptotic analysis method, we obtain the exact expressions of all asymptotic solitons in the vector double-pole solutions. Further, we investigate the characteristics of soliton interactions in the vector double-pole solutions and find some special properties different from the usual vector two-soliton interactions, like each asymptotic soliton is localized in a curve rather than a line, the interacting bright or dark solitons separate from each other in a logarithmical law and the separation acceleration decreases exponentially with the relative distance.