Modulational instability and unstable patterns in the discrete complex cubic Ginzburg-Landau equation with first and second neighbor couplings

作     者：Alidou Mohamadou A. Kenfack Jiotsa T. C. Kofané 

作者机构：Laboratoire de Mécanique Département de Physique Faculté des Sciences Université de Yaoundé I B.P. 812 Yaoundé Cameroun The Abdus Salam International Centre for Theoretical Physics P.O. Box 586 Strada Costiera 11 I-34014 Trieste Italy 

出 版 物：《Physical Review E》 (物理学评论E辑：统计、非线性和软体物理学)

年 卷 期：2005年第72卷第3期

页      面：036220-036220页

核心收录：

学科分类：07[理学] 070203[理学-原子与分子物理] 0702[理学-物理学] 

主　　题：SEMICONDUCTOR-LASER ARRAYS BINARY-FLUID CONVECTION LINEAR-ARRAY WAVE-GUIDES VORTICES SYSTEM ELECTROCONVECTION SELECTION SOLITONS STATES 

摘      要：The generation of nonlinear modulated waves is investigated in the framework of hydrodynamics using a model of coupled oscillators. In this model, the separatrices between each pair of vortices may be viewed as individual oscillators and are described by a phenomenological one-dimensional discrete complex Ginzburg-Landau equation involving first- and second-nearest neighbor couplings. A theoretical approach based on the linear stability analysis predicts regions of modulational instability, governed by both the first and second-nearest neighbor couplings. From numerical investigations of different wave patterns that may be driven by the modulational instability, it appears that analytical predictions are correctly verified. For wave number in the unstable regions, an initial condition whose amplitude is slightly modulated breaks into a train of unstable patterns. This phenomenon agrees with the description of amplification of the spectral component of the perturbation and its harmonics, as well.