TY - JOUR
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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U2 - 10.1016/S0030-4018(03)01457-3
DO - 10.1016/S0030-4018(03)01457-3
M3 - Article
AN - SCOPUS:0037562061
VL - 221
SP - 199
EP - 209
JO - Optics Communications
JF - Optics Communications
SN - 0030-4018
IS - 1-3
ER -