The dynamics of nonautonomous soliton inside planar graded-index waveguide with distributed coefficients

We present a series of exact nonautonomous solitons inside the planar graded-index waveguide amplifier with Kerr nonlinearity by Darboux transformation. Especially, properties of the nonautonomous soliton such as typical width, peak intensity and trajectory of wave center are analytically investigated. We also study the trajectory of wave's center with different conditions in detail. Solitons in planar waveguide without graded-index are also demonstrated.