Inverse Scattering Transform and Solitons for Square Matrix Nonlinear Schrödinger Equations

AbstractThe inverse scattering transform (IST) is developed for a class of matrix nonlinear Schrödinger‐type systems whose reductions include two equations that model certain hyperfine spin spinor Bose–Einstein condensates, and two novel equations that were recently shown to be integrable, and that have applications in nonlinear optics and four‐component fermionic condensates. In addition, the general behavior of the soliton solutions for all four reductions is analyzed in detail, and some novel solutions are presented