Using the inverse-scattering transform with 3×3 U-V matrix representation and fully exploiting the symmetry properties of the scattering matrix elements, we found the one-parameter single-soliton, the four-parameter breather soliton, and the general N-soliton solutions of a perturbed nonlinear Schrödinger equation which describes the femtosecond pulse propagation in optical fibers. The threshold power below which the one-parameter single soliton cannot be formed was given. The main characteristic of the general single-soliton solution of the perturbed nonlinear Schrödinger equation is that it presents an arbitrary number of ‘‘humps’’ (local maxima of the amplitude) of different heights.