Multi-soliton solutions for the coupled nonlinear Schrödinger-type equations

Nonlinear Schrödinger-type equations can model the nonlinear waves in fluids, plasmas, nonlinear optics and atmosphere. In this paper, integrable coupled nonlinear Schrödinger-type equations are investigated. With the aid of symbolic computation, the equations are transformed into their bilinear forms, by virtue of which the multi-soliton solutions are derived. Soliton interactions are analyzed, the elastic interactions are seen, while the dark, anti-dark, M- and W-shape solitons are exhibited with some parameters selected. The propagating solitons can preserve their properties after the interaction, and the profiles of them depend on the corresponding dispersion relations. The amplitudes, velocities of the solitons are found to be influenced by the coefficient of the original equations, which is detailed in the paper.