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

Kenichi Maruno, Adrian Ankiewicz, Nail Akhmediev

Research output: Contribution to journalArticle

44 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 languageEnglish
Pages (from-to)199-209
Number of pages11
JournalOptics Communications
Volume221
Issue number1-3
DOIs
Publication statusPublished - 2003 Jun 1
Externally publishedYes

Fingerprint

Landau-Ginzburg equations
Hamiltonians
Energy balance
Solitons
Phase shift
phase shift
solitary waves
energy

Keywords

  • Discrete complex Ginzburg-Landau equation
  • Dissipative discrete solitons

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

Exact localized and periodic solutions of the discrete complex Ginzburg-Landau equation. / Maruno, Kenichi; Ankiewicz, Adrian; Akhmediev, Nail.

In: Optics Communications, Vol. 221, No. 1-3, 01.06.2003, p. 199-209.

Research output: Contribution to journalArticle

Maruno, Kenichi ; Ankiewicz, Adrian ; Akhmediev, Nail. / Exact localized and periodic solutions of the discrete complex Ginzburg-Landau equation. In: Optics Communications. 2003 ; Vol. 221, No. 1-3. pp. 199-209.
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