Dissipative soliton stabilization by several nonlinear gradient terms

We study a single cubic complex Ginzburg-Landau equation with nonlinear gradient terms analytically and numerically. This single equation allows for the existence of stable dissipative solitons exclusively due to nonlinear gradient terms. We shed new light on the feedback loop, leading to dissipative solitons (DSs) by analyzing a mechanical analog as a function of the magnitude of the amplitude. In addition, we present analytic results incorporating four nonlinear gradient terms and derive necessary conditions for the existence of DSs. We also elucidate in detail for the case of the Raman contribution the scaling behavior for the limit of the vanishing Raman term.