Lax pair and soliton solutions for the generalized nonlinear Schrödinger equation in inhomogeneous optical fiber media

In the paper, a Lax pair is presented for a generalized variable-coefficients nonlinear Schrödinger equation in inhomogeneous optical fiber media with the loss/gain and the frequency chirping. Two types of soliton solutions are constructed by solving its linear non-isospectrum problem. With computer simulation, the main features of bright and dark solitons are shown by some figures. These results will be useful in optical pulse propagation in inhomogeneous optical fiber media.