Solitary waves for two and three coupled nonlinear Schrödinger equations

Abstract

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 ${\mathrm{sech}}^{2}\ensuremath{\xi}\ensuremath{-}\frac{2}{3}$ is found, which, together with two known waves of the forms $\mathrm{tanh}\ensuremath{\xi}\mathrm{sech}\ensuremath{\xi}$ and ${\mathrm{sech}}^{2}\ensuremath{\xi},$ 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.