论文标题
汉堡和KDV方程的平衡状态
Equilibrium states of Burgers and KdV equations
论文作者
论文摘要
我们使用与DELTA相关的随机噪声作为初始条件模拟KDV和无耗散汉堡方程。我们观察到两个方程的能量通量在整个过程中保持零，因此表明它们的平衡性质。我们使用高斯概率分布来表征真实空间场的平衡状态，并使用玻尔兹曼分布来表征模态能量。我们表明，KDV方程的单孤子也表现出零能通量，因此它处于平衡状态。我们认为，能量通量是确定系统是否处于平衡状态的良好方法。
We simulate KdV and dissipation-less Burgers equations using delta-correlated random noise as initial condition. We observe that the energy fluxes of the two equations remain zero throughout, thus indicating their equilibrium nature. We characterize the equilibrium states using Gaussian probability distribution for the real space field, and using Boltzmann distribution for the modal energy. We show that the single soliton of the KdV equation too exhibits zero energy flux, hence it is in equilibrium. We argue that the energy flux is a good measure for ascertaining whether a system is in equilibrium or not.
