Exploding soliton and front solutions of the complex cubic-quintic Ginzburg-Landau equation

J. M. Soto-Crespo; Nail Akhmediev

doi:10.1016/j.matcom.2005.03.006

Exploding soliton and front solutions of the complex cubic-quintic Ginzburg-Landau equation

J. M. Soto-Crespo^*, Nail Akhmediev

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-review

29 Citations (Scopus)

Abstract

We present a study of exploding soliton and front solutions of the complex cubic-quintic Ginzburg-Landau (CGLE) equation. We show that exploding fronts occur in a region of the parameter space close to that where exploding solitons exist. Explosions occur when eigenvalues in the linear stability analysis for the ground-state stationary solitons have positive real parts. We also study transition from exploding fronts to exploding solitons and observed extremely asymmetric soliton explosions.

Original language	English
Pages (from-to)	526-536
Number of pages	11
Journal	Mathematics and Computers in Simulation
Volume	69
Issue number	5-6
DOIs	https://doi.org/10.1016/j.matcom.2005.03.006
Publication status	Published - 5 Aug 2005
Event	Nonlinear Waves: Computation and Theory IV - Duration: 7 Apr 2003 → 10 Apr 2003

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title = "Exploding soliton and front solutions of the complex cubic-quintic Ginzburg-Landau equation",

abstract = "We present a study of exploding soliton and front solutions of the complex cubic-quintic Ginzburg-Landau (CGLE) equation. We show that exploding fronts occur in a region of the parameter space close to that where exploding solitons exist. Explosions occur when eigenvalues in the linear stability analysis for the ground-state stationary solitons have positive real parts. We also study transition from exploding fronts to exploding solitons and observed extremely asymmetric soliton explosions.",

keywords = "Dissipative soliton, Exploding soliton, Ginzburg-Landau equation",

author = "Soto-Crespo, {J. M.} and Nail Akhmediev",

year = "2005",

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doi = "10.1016/j.matcom.2005.03.006",

language = "English",

volume = "69",

pages = "526--536",

journal = "Mathematics and Computers in Simulation",

issn = "0378-4754",

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number = "5-6",

note = "Nonlinear Waves: Computation and Theory IV ; Conference date: 07-04-2003 Through 10-04-2003",

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TY - JOUR

T1 - Exploding soliton and front solutions of the complex cubic-quintic Ginzburg-Landau equation

AU - Soto-Crespo, J. M.

AU - Akhmediev, Nail

PY - 2005/8/5

Y1 - 2005/8/5

N2 - We present a study of exploding soliton and front solutions of the complex cubic-quintic Ginzburg-Landau (CGLE) equation. We show that exploding fronts occur in a region of the parameter space close to that where exploding solitons exist. Explosions occur when eigenvalues in the linear stability analysis for the ground-state stationary solitons have positive real parts. We also study transition from exploding fronts to exploding solitons and observed extremely asymmetric soliton explosions.

AB - We present a study of exploding soliton and front solutions of the complex cubic-quintic Ginzburg-Landau (CGLE) equation. We show that exploding fronts occur in a region of the parameter space close to that where exploding solitons exist. Explosions occur when eigenvalues in the linear stability analysis for the ground-state stationary solitons have positive real parts. We also study transition from exploding fronts to exploding solitons and observed extremely asymmetric soliton explosions.

KW - Dissipative soliton

KW - Exploding soliton

KW - Ginzburg-Landau equation

UR - http://www.scopus.com/inward/record.url?scp=23144467827&partnerID=8YFLogxK

U2 - 10.1016/j.matcom.2005.03.006

DO - 10.1016/j.matcom.2005.03.006

M3 - Conference article

SN - 0378-4754

VL - 69

SP - 526

EP - 536

JO - Mathematics and Computers in Simulation

JF - Mathematics and Computers in Simulation

IS - 5-6

T2 - Nonlinear Waves: Computation and Theory IV

Y2 - 7 April 2003 through 10 April 2003

ER -

Exploding soliton and front solutions of the complex cubic-quintic Ginzburg-Landau equation

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