Exact Solutions for Domain Walls in Coupled Complex Ginzburg--Landau Equations
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概要
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The complex Ginzburg--Landau equation (CGLE) is a ubiquitous model for the evolution of slowly varying wave packets in nonlinear dissipative media. A front (shock) is a transient layer between a plane-wave state and a zero background. We report exact solutions for domain walls, i.e., pairs of fronts with opposite polarities, in a system of two coupled CGLEs, which describe transient layers between semi-infinite domains occupied by each component in the absence of the other one. For this purpose, a modified Hirota bilinear operator, first proposed by Bekki and Nozaki, is employed. A novel factorization procedure is applied to reduce the intermediate calculations considerably. The ensuing system of equations for the amplitudes and frequencies is solved by means of computer-assisted algebra. Exact solutions for mutually-locked front pairs of opposite polarities, with one or several free parameters, are thus generated. The signs of the cubic gain/loss, linear amplification/attenuation, and velocity of the coupled-front complex can be adjusted in a variety of configurations. Numerical simulations are performed to study the stability properties of such fronts.
- 2011-06-15
著者
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Chow Kwok
Department Of Mathematics University Of Arizona
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Malomed Boris
Department Of Interdisciplinary Studies Faculty Of Engineering Tel Aviv University
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Yee Tat
Department of Mathematics and Information Technology, Hong Kong Institute of Education, Tai Po, New Territories, Hong Kong
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Chow Kwok
Department of Mechanical Engineering, University of Hong Kong, Pokfulam, Hong Kong
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Tsang Alan
Department of Mechanical Engineering, University of Hong Kong, Pokfulam, Hong Kong
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Malomed Boris
Department of Applied Mathematics, School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University
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Malomed Boris
Department of Physical Electronics, School of Electrical Engineering, Tel Aviv University, Tel Aviv 69978, Israel
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