Macroscopic dynamics of incoherent soliton ensembles: Soliton gas kinetics and direct numerical modelling
Macroscopic dynamics of incoherent soliton ensembles: Soliton gas kinetics and direct numerical modelling
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DOI：
10.1209/0295-5075/113/30003
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发表时间：
2016-02-01
期刊：
影响因子：
1.8
通讯作者：
El, G. A.
中科院分区：
文献类型：
--
作者：
Carbone, F.;Dutykh, D.;El, G. A.
我们进行了详细的比较Korteweg-de弗里斯方程的孤子气体动力学的直接数值模拟的结果与分析预测推断的孤子的相关动力学方程的精确解。考虑了两个模型问题：i）“试验”孤子通过由随机分布的振幅近似相同的孤子组成的单组分“冷”孤子气体的传播; ii）两个振幅不同的冷孤子气体的碰撞（孤子气体激波管问题）导致形成膨胀的非相干色散激波。在这两种情况下，观察孤子气体动力学的分析预测和直接的数值模拟之间的良好的协议。我们的研究结果证实了孤子的动力学方程的相关性作为一个定量准确的模型宏观非平衡动力学的非相干孤子系综。版权所有（C）2016 EPLA
We undertake a detailed comparison of the results of direct numerical simulations of the soliton gas dynamics for the Korteweg-de Vries equation with the analytical predictions inferred from the exact solutions of the relevant kinetic equation for solitons. Two model problems are considered: i) the propagation of a "trial" soliton through a one-component "cold" soliton gas consisting of randomly distributed solitons of approximately the same amplitude; and ii) the collision of two cold soliton gases of different amplitudes (the soliton gas shock tube problem) leading to the formation of an expanding incoherent dispersive shock wave. In both cases excellent agreement is observed between the analytical predictions of the soliton gas kinetics and the direct numerical simulations. Our results confirm the relevance of the kinetic equation for solitons as a quantitatively accurate model for macroscopic non-equilibrium dynamics of incoherent soliton ensembles. Copyright (C) EPLA, 2016