Summary: Exact localized and periodic solutions of the discrete complex
Ginzburg­Landau equation
Ken-ichi Marunoa,c,*, Adrian Ankiewiczb
, Nail Akhmedievc
a
Research Institute for Applied Mechanics, Kyushu University, Kasuga, Fukuoka, 816-8580, Japan
b
Applied Photonics Group, Research School of Physical Sciences and Engineering, The Australian National University,
Canberra ACT 0200, Australia
c
Optical Sciences Centre, Research School of Physical Sciences and Engineering, The Australian National University,
Canberra ACT 0200, Australia
Received 6 March 2003; received in revised form 14 April 2003; accepted 14 April 2003
Abstract
We study, analytically, the discrete complex cubic Ginzburg­Landau (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.

Source: Akhmediev, Nail - Research School of Physical Sciences and Engineering, Australian National University
Australian National University, Research School of Physical Sciences and Engineering, Optical Sciences Group

Collections: Engineering; Physics