Exact localized and periodic solutions of the discrete complex Ginzburg-Landau equation

Ken ichi Maruno; Adrian Ankiewicz; Nail Akhmediev

doi:10.1016/S0030-4018(03)01457-3

Exact localized and periodic solutions of the discrete complex Ginzburg-Landau equation

Ken ichi Maruno^*, Adrian Ankiewicz, Nail Akhmediev

^*Corresponding author for this work

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

48 Citations (Scopus)

Abstract

We study, analytically, the discrete complex cubic Ginzburg-Landau (dCCGL) equation. We derive the energy balance equation for the dCCGL and consider various limiting cases. We have found a set of exact solutions which includes as particular cases periodic solutions in terms of elliptic Jacobi functions, bright and dark soliton solutions, and constant magnitude solutions with phase shifts. We have also found the range of parameters where each exact solution exists. We discuss the common features of these solutions and solutions of the continuous complex Ginzburg-Landau model and solutions of Hamiltonian discrete systems and also their differences.

Original language	English
Pages (from-to)	199-209
Number of pages	11
Journal	Optics Communications
Volume	221
Issue number	1-3
DOIs	https://doi.org/10.1016/S0030-4018(03)01457-3
Publication status	Published - 2003 Jun 1
Externally published	Yes

Keywords

Discrete complex Ginzburg-Landau equation
Dissipative discrete solitons

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Atomic and Molecular Physics, and Optics
Physical and Theoretical Chemistry
Electrical and Electronic Engineering

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10.1016/S0030-4018(03)01457-3

Cite this

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title = "Exact localized and periodic solutions of the discrete complex Ginzburg-Landau equation",

abstract = "We study, analytically, the discrete complex cubic Ginzburg-Landau (dCCGL) equation. We derive the energy balance equation for the dCCGL and consider various limiting cases. We have found a set of exact solutions which includes as particular cases periodic solutions in terms of elliptic Jacobi functions, bright and dark soliton solutions, and constant magnitude solutions with phase shifts. We have also found the range of parameters where each exact solution exists. We discuss the common features of these solutions and solutions of the continuous complex Ginzburg-Landau model and solutions of Hamiltonian discrete systems and also their differences.",

keywords = "Discrete complex Ginzburg-Landau equation, Dissipative discrete solitons",

author = "Maruno, {Ken ichi} and Adrian Ankiewicz and Nail Akhmediev",

note = "Funding Information: K.M. was supported by a JSPS Fellowship for Young Scientists. N.A. acknowledges support from the Australian Research Council. Copyright: Copyright 2004 Elsevier Science B.V., Amsterdam. All rights reserved.",

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doi = "10.1016/S0030-4018(03)01457-3",

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T1 - Exact localized and periodic solutions of the discrete complex Ginzburg-Landau equation

AU - Maruno, Ken ichi

AU - Ankiewicz, Adrian

AU - Akhmediev, Nail

N1 - Funding Information: K.M. was supported by a JSPS Fellowship for Young Scientists. N.A. acknowledges support from the Australian Research Council. Copyright: Copyright 2004 Elsevier Science B.V., Amsterdam. All rights reserved.

PY - 2003/6/1

Y1 - 2003/6/1

N2 - We study, analytically, the discrete complex cubic Ginzburg-Landau (dCCGL) equation. We derive the energy balance equation for the dCCGL and consider various limiting cases. We have found a set of exact solutions which includes as particular cases periodic solutions in terms of elliptic Jacobi functions, bright and dark soliton solutions, and constant magnitude solutions with phase shifts. We have also found the range of parameters where each exact solution exists. We discuss the common features of these solutions and solutions of the continuous complex Ginzburg-Landau model and solutions of Hamiltonian discrete systems and also their differences.

AB - We study, analytically, the discrete complex cubic Ginzburg-Landau (dCCGL) equation. We derive the energy balance equation for the dCCGL and consider various limiting cases. We have found a set of exact solutions which includes as particular cases periodic solutions in terms of elliptic Jacobi functions, bright and dark soliton solutions, and constant magnitude solutions with phase shifts. We have also found the range of parameters where each exact solution exists. We discuss the common features of these solutions and solutions of the continuous complex Ginzburg-Landau model and solutions of Hamiltonian discrete systems and also their differences.

KW - Discrete complex Ginzburg-Landau equation

KW - Dissipative discrete solitons

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JO - Optics Communications

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Exact localized and periodic solutions of the discrete complex Ginzburg-Landau equation

Abstract

Keywords

ASJC Scopus subject areas

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