The transition to explosive solitons and the destruction of invariant tori

Jaime Cisternas; Orazio Descalzi; Carlos Cartes

doi:10.2478/s11534-012-0023-1

The transition to explosive solitons and the destruction of invariant tori

Jaime Cisternas, Orazio Descalzi^*, Carlos Cartes

^*Corresponding author for this work

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

4 Scopus citations

Abstract

We investigate the transition to explosive dissipative solitons and the destruction of invariant tori in the complex cubic-quintic Ginzburg-Landau equation in the regime of anomalous linear dispersion as a function of the distance from linear onset. Using Poncaré sections, we sequentially find fixed points, quasiperiodicity (two incommesurate frequencies), frequency locking, two torus-doubling bifurcations (from a torus to a 2-fold torus and from a 2-fold torus to a 4-fold torus), the destruction of a 4-fold torus leading to non-explosive chaos, and finally explosive solitons. A narrow window, in which a 3-fold torus appears, is also observed inside the chaotic region.

Original language	English
Pages (from-to)	660-668
Number of pages	9
Journal	Central European Journal of Physics
Volume	10
Issue number	3
DOIs	https://doi.org/10.2478/s11534-012-0023-1
State	Published - Jun 2012

Bibliographical note

Funding Information:
The authors acknowldge support from FONDECYT under project No. 1110360 and project No. 3110028 as well as from the Universidad de los Andes through FAI initiatives.

Keywords

cubic-quintic Ginzburg-Landau equation
destruction of invariant tori
explosive dissipative solitons

Access to Document

10.2478/s11534-012-0023-1

Cite this

@article{41e36167e44b4e5c81c66c6fdbeb75a0,

title = "The transition to explosive solitons and the destruction of invariant tori",

abstract = "We investigate the transition to explosive dissipative solitons and the destruction of invariant tori in the complex cubic-quintic Ginzburg-Landau equation in the regime of anomalous linear dispersion as a function of the distance from linear onset. Using Poncar{\'e} sections, we sequentially find fixed points, quasiperiodicity (two incommesurate frequencies), frequency locking, two torus-doubling bifurcations (from a torus to a 2-fold torus and from a 2-fold torus to a 4-fold torus), the destruction of a 4-fold torus leading to non-explosive chaos, and finally explosive solitons. A narrow window, in which a 3-fold torus appears, is also observed inside the chaotic region.",

keywords = "cubic-quintic Ginzburg-Landau equation, destruction of invariant tori, explosive dissipative solitons, Cubic-quintic Ginzburg-Landau equation, Destruction of invariant tori, Explosive dissipative solitons",

author = "Jaime Cisternas and Orazio Descalzi and Carlos Cartes",

note = "Funding Information: The authors acknowldge support from FONDECYT under project No. 1110360 and project No. 3110028 as well as from the Universidad de los Andes through FAI initiatives.",

year = "2012",

month = jun,

doi = "10.2478/s11534-012-0023-1",

language = "English",

volume = "10",

pages = "660--668",

journal = "Central European Journal of Physics",

issn = "1895-1082",

publisher = "Walter de Gruyter GmbH",

number = "3",

}

TY - JOUR

T1 - The transition to explosive solitons and the destruction of invariant tori

AU - Cisternas, Jaime

AU - Descalzi, Orazio

AU - Cartes, Carlos

N1 - Funding Information: The authors acknowldge support from FONDECYT under project No. 1110360 and project No. 3110028 as well as from the Universidad de los Andes through FAI initiatives.

PY - 2012/6

Y1 - 2012/6

N2 - We investigate the transition to explosive dissipative solitons and the destruction of invariant tori in the complex cubic-quintic Ginzburg-Landau equation in the regime of anomalous linear dispersion as a function of the distance from linear onset. Using Poncaré sections, we sequentially find fixed points, quasiperiodicity (two incommesurate frequencies), frequency locking, two torus-doubling bifurcations (from a torus to a 2-fold torus and from a 2-fold torus to a 4-fold torus), the destruction of a 4-fold torus leading to non-explosive chaos, and finally explosive solitons. A narrow window, in which a 3-fold torus appears, is also observed inside the chaotic region.

AB - We investigate the transition to explosive dissipative solitons and the destruction of invariant tori in the complex cubic-quintic Ginzburg-Landau equation in the regime of anomalous linear dispersion as a function of the distance from linear onset. Using Poncaré sections, we sequentially find fixed points, quasiperiodicity (two incommesurate frequencies), frequency locking, two torus-doubling bifurcations (from a torus to a 2-fold torus and from a 2-fold torus to a 4-fold torus), the destruction of a 4-fold torus leading to non-explosive chaos, and finally explosive solitons. A narrow window, in which a 3-fold torus appears, is also observed inside the chaotic region.

KW - cubic-quintic Ginzburg-Landau equation

KW - destruction of invariant tori

KW - explosive dissipative solitons

KW - Cubic-quintic Ginzburg-Landau equation

KW - Destruction of invariant tori

KW - Explosive dissipative solitons

UR - http://www.scopus.com/inward/record.url?scp=84862597095&partnerID=8YFLogxK

U2 - 10.2478/s11534-012-0023-1

DO - 10.2478/s11534-012-0023-1

M3 - Article

AN - SCOPUS:84862597095

SN - 1895-1082

VL - 10

SP - 660

EP - 668

JO - Central European Journal of Physics

JF - Central European Journal of Physics

IS - 3

ER -

The transition to explosive solitons and the destruction of invariant tori

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this