Simultaneous existence of a multiplicity of stable and unstable solitons in dissipative systems

J. M. Soto-Crespo; Nail Akhmediev; Kin S. Chiang

doi:10.1016/S0375-9601(01)00634-X

Simultaneous existence of a multiplicity of stable and unstable solitons in dissipative systems

J. M. Soto-Crespo^*
, Nail Akhmediev
, Kin S. Chiang

^*Corresponding author for this work

Department of Electrical Engineering

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

51 Citations (Scopus)

Abstract

We show that dissipative systems can have a multiplicity of stationary solutions in the form of both stable and unstable solitons. As a model equation, we use the complex cubic-quintic Ginzburg-Landau equation. For a given set of the equation parameters, this equation has many coexisting soliton solutions. Our stability results show that although most of them are unstable, they can have stable pieces. This partial stability leads to the phenomenon of soliton explosion. © 2001 Elsevier Science B.V. All rights reserved.

Original language	English
Pages (from-to)	115-123
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	291
Issue number	2-3
DOIs	https://doi.org/10.1016/S0375-9601(01)00634-X
Publication status	Published - 3 Dec 2001

Research Keywords

Dissipative systems
Ginzburg-Landau equation
Solitons

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10.1016/S0375-9601(01)00634-X

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title = "Simultaneous existence of a multiplicity of stable and unstable solitons in dissipative systems",

abstract = "We show that dissipative systems can have a multiplicity of stationary solutions in the form of both stable and unstable solitons. As a model equation, we use the complex cubic-quintic Ginzburg-Landau equation. For a given set of the equation parameters, this equation has many coexisting soliton solutions. Our stability results show that although most of them are unstable, they can have stable pieces. This partial stability leads to the phenomenon of soliton explosion. {\textcopyright} 2001 Elsevier Science B.V. All rights reserved.",

keywords = "Dissipative systems, Ginzburg-Landau equation, Solitons",

author = "Soto-Crespo, \{J. M.\} and Nail Akhmediev and Chiang, \{Kin S.\}",

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Simultaneous existence of a multiplicity of stable and unstable solitons in dissipative systems. / Soto-Crespo, J. M.; Akhmediev, Nail; Chiang, Kin S.
In: Physics Letters, Section A: General, Atomic and Solid State Physics, Vol. 291, No. 2-3, 03.12.2001, p. 115-123.

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

TY - JOUR

T1 - Simultaneous existence of a multiplicity of stable and unstable solitons in dissipative systems

AU - Soto-Crespo, J. M.

AU - Akhmediev, Nail

AU - Chiang, Kin S.

PY - 2001/12/3

Y1 - 2001/12/3

N2 - We show that dissipative systems can have a multiplicity of stationary solutions in the form of both stable and unstable solitons. As a model equation, we use the complex cubic-quintic Ginzburg-Landau equation. For a given set of the equation parameters, this equation has many coexisting soliton solutions. Our stability results show that although most of them are unstable, they can have stable pieces. This partial stability leads to the phenomenon of soliton explosion. © 2001 Elsevier Science B.V. All rights reserved.

AB - We show that dissipative systems can have a multiplicity of stationary solutions in the form of both stable and unstable solitons. As a model equation, we use the complex cubic-quintic Ginzburg-Landau equation. For a given set of the equation parameters, this equation has many coexisting soliton solutions. Our stability results show that although most of them are unstable, they can have stable pieces. This partial stability leads to the phenomenon of soliton explosion. © 2001 Elsevier Science B.V. All rights reserved.

KW - Dissipative systems

KW - Ginzburg-Landau equation

KW - Solitons

UR - https://www.scopus.com/pages/publications/0035803625

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-0035803625&origin=recordpage

U2 - 10.1016/S0375-9601(01)00634-X

DO - 10.1016/S0375-9601(01)00634-X

M3 - RGC 21 - Publication in refereed journal

SN - 0375-9601

VL - 291

SP - 115

EP - 123

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 2-3

ER -

Simultaneous existence of a multiplicity of stable and unstable solitons in dissipative systems

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