Solitary waves for two and three coupled nonlinear Schrödinger equations

We present solitary-wave solutions of two and three coupled nonlinear Schrödinger equations when the waves propagate in the normal and anomalous group-velocity dispersion regions. A wave of the form ${\mathrm{sech}}^2\xi -\frac{2}{3}$ is found, which, together with two known waves of the forms $\tanh \xi \mathrm{sech}\xi$ and ${\mathrm{sech}}^2\xi ,$ 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.