论文标题
盒球系统的广义流体动力极限
Generalized hydrodynamic limit for the box-ball system
论文作者
论文摘要
我们推断出盒球系统的广义流体力学极限，该系统解释了在Euler时空扩展下如何渐近地演化的不同尺寸的孤子的密度如何。为了描述有限的孤子流，我们介绍了法拉利，Nguyen，Rolla和Wang的孤子分解的连续状态空间类似物（参见Takahashi和Satsuma的原始作品），即，我们介绍了在尺寸上，在尺度上相应的尺寸密度在尺度上，我们将尺寸的尺寸密度固定在尺度上，从而有效地有效。对于平滑的初始条件，我们进一步表明，空间中孤子密度的产生演变可以以部分微分方程为特征，该方程自然地将孤子密度的时间衍生物和本地孤子的“有效速度”联系起来。
We deduce a generalized hydrodynamic limit for the box-ball system, which explains how the densities of solitons of different sizes evolve asymptotically under Euler space-time scaling. To describe the limiting soliton flow, we introduce a continuous state-space analogue of the soliton decomposition of Ferrari, Nguyen, Rolla and Wang (cf. the original work of Takahashi and Satsuma), namely we relate the densities of solitons of given sizes in space to corresponding densities on a scale of 'effective distances', where the dynamics are linear. For smooth initial conditions, we further show that the resulting evolution of the soliton densities in space can alternatively be characterised by a partial differential equation, which naturally links the time-derivatives of the soliton densities and the 'effective speeds' of solitons locally.
