Solitary waves for two and three coupled nonlinear Schrödinger equations

We present solitary-wave solutions of two and three coupled nonlinear Schr\"odinger equations when the waves propagate in the normal and anomalous group-velocity dispersion regions. A wave of the form sech²ξ-2/3 is found, which, together with two known waves of the forms tanhξsechξ and sech²ξ, are shown to form a new generation of complementary waves. The implication of this wave set and its applications to coupled solitary-wave propagation is discussed.