Integrability and soliton solutions for an N-coupled nonlinear Schrödinger system in optical fibers

In this paper, an N-coupled nonlinear Schrödinger system in optical fibers with energy-exchanging and different self-phase modulation and cross-phase modulation terms is investigated. The system is found to be integrable in the sense of passing the Painlevé analysis. The Lax pair for the system is given in the form of the block matrices through generalizing that for a 2-coupled nonlinear Schrödinger system with the Ablowitz–Kaup–Newell–Segur scheme. Through the Hirota bilinear method with an auxiliary function, one- and two-soliton solutions are derived via symbolic computation. One-soliton solutions can present the profile of one peak or two peaks in different components. With the asymptotic analysis, two-soliton solutions are found to admit the elastic collision, and the propagation and collision of solitons are analyzed.