Effect of nonlinear gradient terms on pulsating, erupting and creeping solitons

The effect of nonlinear gradient terms on the pulsating, erupting and creeping solitons, respectively, of the cubic-quintic complex Ginzburg-Landau equation is investigated. It is found that the nonlinear gradient terms result in dramatic changes in the soliton behavior. They eliminate the periodicity of the pulsating and erupting solitons and transform them into fixed-shape solitons. This is important for potential use, such as to realize experimentally the undistorted transmission of femtosecond pulses in optical fibers. However, the nonlinear gradient terms cause the creeping soliton to breathe periodically at different frequencies on one side and spread rapidly on the other side.