Algebraically decaying pulses in a Ginzburg–Landau system with a neutrally stable mode
Algebraically decaying pulses in a Ginzburg–Landau system with a neutrally stable mode
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DOI：
10.1088/0951-7715/20/2/007
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发表时间：
2007-01
期刊：
影响因子：
1.7
通讯作者：
A. Doelman;G. Hek;N. Valkhoff
中科院分区：
文献类型：
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作者：
A. Doelman;G. Hek;N. Valkhoff
本文研究了具有相互作用不稳定机制的系统中脉冲解的存在性和稳定性，该系统用a模的Ginzburg-Landau方程和b模的扩散方程耦合来描述。我们的主要问题是，当与中性稳定b模的相互作用不包括在模型中时，这种耦合是否可以稳定金兹堡-朗道方程的不稳定解。空间均匀的b模被认为是中性稳定的。这意味着脉冲解不能呈指数衰减，而必须以x→±∞的代数速率衰减。因此，现有的研究奇摄动反应扩散系统中脉冲稳定性的方法需要得到扩展。这导致了一种“代数NLEP方法”，预计它将超出本文的设定。在（弱）稳定b模的情况下（Doelman et al . 2004）。Sci. 14 237-78)我们通过这种方法的应用建立了b模式确实引入了一种机制，可以稳定当不考虑与b模式的相互作用时不稳定的脉冲。
In this paper, we study the existence and stability of pulse solutions in a system with interacting instability mechanisms, which is described by a Ginzburg–Landau equation for an A-mode, coupled to a diffusion equation for a B-mode. Our main question is whether this coupling may stabilize solutions of the Ginzburg–Landau equation that are unstable when the interactions with the neutrally stable B-mode are not included in the model. The spatially homogeneous B-mode is supposed to be neutrally stable. This implies that the pulse solutions cannot decay exponentially, but must decay with an algebraic rate as x → ±∞. As a consequence, the methods that exist in the literature by which the stability of pulses in singularly perturbed reaction–diffusion systems can be studied need to be extended. This results in an ‘algebraic NLEP approach’, which is expected to be relevant beyond the setting of this paper. As in the case of a (weakly) stable B-mode (Doelman et al 2004 J. Nonlin. Sci. 14 237–78) we establish by the application of this approach that the B-mode indeed introduces a mechanism that may stabilize pulses that are unstable when the interactions with the B-mode are not taken into account.