Formation of the amplification regime of quasi-soliton pulses in waveguides with longitudinally inhomogeneous cross sections

The possibility of ideal soliton amplification in a waveguide due to the formation of a specific inhomogeneity of its radius along the length is studied using the example of an active gradient-index (with a parabolic profile of the refractive index) optical fiber. It is shown that, in the case of an appropriate choice of the a(z) function, such soliton dynamics is possible even if the gain increment is constant over the length. The conditions imposed on the frequency dependences of the parameters determining the soliton dynamics are considered.