Dark single- and double-hump vector solitons of the coupled higher-order nonlinear Schrödinger equations in the birefringent or two-mode fibers

Dark vector solitons of the coupled higher-order nonlinear Schrödinger equations, which describe the ultrashort pulse propagation in the birefringent or two-mode fiber, are investigated. By means of the Hirota method, we construct the anti-dark, dark single- and double-hump vector soliton solutions. Parametric regions for the existence of such vector soliton solutions are given, which are related to the third-order dispersion (TOD) and self-steepening (SS). Graphical analysis shows that the amplitudes of the dark single-hump and anti-dark vector solitons can be influenced by the ratio of the TOD to SS, while the amplitudes of the dark double-hump vector solitons keep invariant. With the TOD and SS coefficients changing, interactions between the two anti-dark solitons, two dark double-hump solitons, two dark single-hump solitons or dark single-hump and dark double-hump solitons are studied. Asymptotic analysis shows that such interactions are elastic.