Integrable conditions and inhomogeneous soliton solutions of a coupled nonlinear Schrödinger system with distributed coefficients

Considering the optical solitons propagation in inhomogeneous birefringent fibers, we study a coupled nonlinear Schrödinger system with distributed coefficients. First, we identify the integrable cases for this system to pass the Painlevé test and admit the Lax pair. Then, we explicitly construct the N-th iterated Darboux transformation and algebraically derive the triple Wronskian solutions which imply the inhomogeneous bright–bright N-soliton solutions. Finally, we reveal some propagation and interaction features of inhomogeneous solitons: (a) the linear fiber loss/gain causes the amplitudes to decay/grow exponentially, (b) variable dispersion leads to the nonuniform propagation of solitons and the possibility for two solitons to interact more than one time at different locations, and (c) the energy-exchanging interactions can conditionally occur between two components for each pair of interacting solitons.