Dark solitons in N-coupled higher order nonlinear Schrِdinger equations

By considering the third order dispersion, self-steepening and stimulated Raman scattering effects, we analyse the dark soliton propagation in N-coupled higher order nonlinear Schrِdinger equations. Using Painlevé analysis, we prove that this system is completely integrable. The result is confirmed further by the presentation of Lax pair. Using the Hirota method, the construction of soliton solution is discussed.