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.
Bibliographical noteFunding Information:
O.D. wishes to acknowledge the support of the FONDECYT (CL) (Nos. 1170728 and 1200357) and the Universidad de los Andes through FAI initiatives. H.R.B. thanks the Deutsche Forschungsge-meinschaft (DE) for partial support of this work. It is a great pleasure to dedicate this work to Professor Enrique Tirapegui on the occasion of his 80th birthday.
© 2020 Author(s).