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
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
UR - http://www.scopus.com/inward/record.url?scp=0037562061&partnerID=8YFLogxK
U2 - 10.1016/S0030-4018(03)01457-3
DO - 10.1016/S0030-4018(03)01457-3
M3 - Article
SN - 0030-4018
VL - 221
SP - 199
EP - 209
JO - Optics Communications
JF - Optics Communications
IS - 1-3
ER -