Integrability aspects with optical solitons of a generalized variable-coefficient N-coupled higher order nonlinear Schrödinger system from inhomogeneous optical fibers

For describing the long-distance communication and manufacturing problems of N fields propagation in inhomogeneous optical fibers, we consider a generalized variable-coefficient N-coupled nonlinear Schrödinger system with higher order effects such as the third-order dispersion, self-steepening and self-frequency shift. Using the Painlevé singularity structure analysis, we obtain two cases for this system to admit the Painlevé property. Then for case (1) we derive the optical dark solitons via solving the Hirota bilinear equations; and based on the obtained (2N+1)×(2N+1) Lax pair, we construct the Darboux transformation to obtain the optical bright solitons (including the multisoliton profiles) for case (2). Finally, the features of optical solitons (both dark and bright ones) in inhomogeneous optical fibers are analyzed and graphically discussed.