Dissipative soliton stabilization by several nonlinear gradient terms

Orazio Descalzi; Helmut R. Brand

doi:10.1063/1.5145280

Dissipative soliton stabilization by several nonlinear gradient terms

Orazio Descalzi^*, Helmut R. Brand

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

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.

Translated title of the contribution	Estabilización de solitones disipativos mediante varios términos de gradiente no lineal
Original language	English
Article number	043119
Journal	Chaos
Volume	30
Issue number	4
DOIs	https://doi.org/10.1063/1.5145280
State	Published - 1 Apr 2020

Bibliographical note

Funding 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.

Publisher Copyright:
© 2020 Author(s).

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title = "Dissipative soliton stabilization by several nonlinear gradient terms",

abstract = "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.",

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N2 - 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.

AB - 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.

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Dissipative soliton stabilization by several nonlinear gradient terms

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