Solitary Waves forNCoupled Nonlinear Schrödinger Equations

A hierarchy of exact analytic solitary-wave solutions for $N$ coupled nonlinear Schrödinger equations for which the nonlinear coupling parameters can change continuously and cover many regions is presented. Besides their potentially many practical applications to optical communication and multispecies Bose-Einstein condensates for couplings outside the special integrable cases, these analytically solvable cases for special initial conditions supplement and provide important links to and among the integrable cases.