Kim Jong-Won, Ott Edward
Department of Physics, and Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD 20742, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Feb;67(2 Pt 2):026203. doi: 10.1103/PhysRevE.67.026203. Epub 2003 Feb 5.
We study the statistics and characteristics of rare intense events in two types of two-dimensional complex Ginzburg-Landau (CGL) equation based models. Our numerical simulations show finite amplitude collapselike solutions which approach the infinite amplitude solutions of the nonlinear Schrödinger equation in an appropriate parameter regime. We also determine the probability distribution function of the amplitude of the CGL solutions, which is found to have enhanced (as compared to Gaussian) probability for the amplitude to be large. Our results suggest a general picture in which an incoherent background of weakly interacting waves, occasionally, "by chance," initiates intense, coherent, self-reinforcing, highly nonlinear events.
我们研究了基于两种二维复金兹堡 - 朗道（CGL）方程模型中罕见强烈事件的统计特性。我们的数值模拟显示，在适当的参数范围内，有限振幅的类坍缩解趋近于非线性薛定谔方程的无限振幅解。我们还确定了CGL解振幅的概率分布函数，发现该函数对于大振幅具有比高斯分布增强的概率。我们的结果表明了一种总体情况，即弱相互作用波的非相干背景偶尔会“偶然地”引发强烈、相干、自我增强的高度非线性事件。
