  We present the exact bright one-soliton and two-soliton solutions of the
integrable three coupled nonlinear Schroedinger equations (3-CNLS) by using the
Hirota method, and then obtain them for the general $N$-coupled nonlinear
Schroedinger 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 analyse the various possibilities and conditions for
such collisions to occur. Further, we report the significant fact that the
various partial coherent solitons (PCS) discussed in the literature are special
cases of the higher order bright soliton solutions of the N-CNLS equations.
