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

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

50 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.

Original language	English
Pages (from-to)	115-123
Number of pages	9
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

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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.",

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

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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.

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.

KW - Dissipative systems

KW - Ginzburg-Landau equation

KW - Solitons

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

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

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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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