论文标题
非线性非局部模型的金茨堡 - 陆幅度方程
Ginzburg-Landau amplitude equation for nonlinear nonlocal models
论文作者
论文摘要
常规空间结构以局部和/或非局部耦合项为特征的各种不同的动力学出现。在几个研究领域，这刺激了许多模型的研究，这可以解释模式形成。线性近似分析无法捕获在长空间和时间尺度上发生的模式的调制。在这里，我们表明，从具有远距离耦合显示模式的通用模型开始，在不稳定性开始时大规模调制的时空演化是由众所周知的Ginzburg-Landau方程所统治的，独立于动力学的细节。因此，我们在描述了广泛的系统的行为中证明了这种方程的有效性。我们介绍了一个新型的数学框架，该框架还能够检索Ginzburg-Landau方程中出现的系数的分析表达式作为模型参数的函数。这种框架可以包括高阶非局部相互作用，并且适用性比此处考虑的模型更大，可能包括具有非常不同物理特征的模型中的模式形成。
Regular spatial structures emerge in a wide range of different dynamics characterized by local and/or nonlocal coupling terms. In several research fields this has spurred the study of many models, which can explain pattern formation. The modulations of patterns, occurring on long spatial and temporal scales, can not be captured by linear approximation analysis. Here, we show that, starting from a general model with long range couplings displaying patterns, the spatio-temporal evolution of large scale modulations at the onset of instability is ruled by the well-known Ginzburg-Landau equation, independently of the details of the dynamics. Hence, we demonstrate the validity of such equation in the description of the behavior of a wide class of systems. We introduce a novel mathematical framework that is also able to retrieve the analytical expressions of the coefficients appearing in the Ginzburg-Landau equation as functions of the model parameters. Such framework can include higher order nonlocal interactions and has much larger applicability than the model considered here, possibly including pattern formation in models with very different physical features.
