Exact Soliton Solutions, Shape Changing Collisions, and Partially Coherent Solitons in Coupled Nonlinear Schrödinger Equations

We present the exact bright one-soliton and two-soliton solutions of the integrable three coupled nonlinear Schrödinger equations (3-CNLS) by using the Hirota method, and then obtain them for the general $N$-coupled nonlinear Schrödinger equations ( $N$-CNLS). It is pointed out that the underlying solitons undergo inelastic (shape changing) collisions due to intensity redistribution among the modes. We also analyze the various possibilities and conditions for such collisions to occur. Further, we report the significant fact that the various partially coherent solitons discussed in the literature are special cases of the higher order bright soliton solutions of the $N$-CNLS equations.