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 journalArticlepeer-review

50 Citations (Scopus)


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
Issue number1-3
Publication statusPublished - 2003 Jun 1
Externally publishedYes


  • 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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