Conservation laws, vector solitons and breathers of a generalized variable-coefficient N-coupled higher-order nonlinear Schrödinger system from inhomogeneous optical fibers

To describe the long-distance communication and manufacturing problems of N fields optical solitons propagating simultaneously in inhomogeneous optical fibers, we study a generalized variable-coefficient N-coupled nonlinear Schrödinger system with higher-order effects, where N is a positive integer. We obtain the infinitely-many conservation laws and the N-Fold Darboux-dressing transformation. Via the N-Fold Darboux-dressing transformation, we give the one-, two- and N-dark-bright soliton solutions, and the first and Nth-order breather solutions. We find that: (1) the coefficients in equation, group velocity, f(z), affects the velocity of soliton; (2) third-order dispersion, c(z), affects the velocity and background of soliton and breather, and (3) self-steepening, d(z), affects the background of breather.