Integrable aspects and applications of a generalized inhomogeneous N-coupled nonlinear Schrödinger system in plasmas and optical fibers via symbolic computation

For describing the general behavior of N fields propagating in inhomogeneous plasmas and optical fibers, a generalized N-coupled nonlinear Schrödinger system is investigated with symbolic computation in this Letter. When the coefficient functions obey the Painlevé-integrable conditions, the (N+1)×(N+1) nonisospectral Lax pair associated with such a model is derived by means of the Ablowitz–Kaup–Newell–Segur formalism. Furthermore, the Darboux transformation is constructed so that it becomes exercisable to generate the multi-soliton solutions in a recursive manner. Through the graphical analysis of some exact analytic one- and two-soliton solutions, our discussions are focused on the envelope soliton excitation in time-dependent inhomogeneous plasmas and the optical pulse propagation with the constant (or distance-related) fiber gain/loss and phase modulation.