Mixed-type solitons for the coupled higher-order nonlinear Schrödinger equations in multi-mode and birefringent fibers

In this paper, coupled higher-order nonlinear Schrödinger equations are studied for the ultrashort pulse propagation in such optical media as the multi-mode fibers and birefringent fibers. Through the Hirota method and symbolic computation, analytic mixed-type one- and two-soliton solutions are derived, and three sets of conditions for the non-singular solutions are given as well. Via the one-soliton solutions obtained, critical condition for the black and gray solitons is obtained analytically. Asymptotic analysis is carried out on the two-soliton solutions to derive the condition for the inelastic interaction. Evolution of the bound vector solitons, elastic and inelastic interactions between the two vector solitons are also investigated graphically. Moreover, after the inelastic interaction, the two bright solitons are observed to disappear, while the two dark ones form the new bound soliton.