Kinetic Equation for a Soliton Gas and Its Hydrodynamic Reductions
Kinetic Equation for a Soliton Gas and Its Hydrodynamic Reductions
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DOI：
10.1007/s00332-010-9080-z
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发表时间：
2011-04-01
影响因子：
3
通讯作者：
Zykov, S. A.
中科院分区：
文献类型：
--
作者：
El, G. A.;Kamchatnov, A. M.;Zykov, S. A.
本文引入并研究了一类新的动力学方程，该方程是在描述孤子间弹性碰撞的孤子气体的非平衡宏观动力学过程中产生的。这些方程代表非线性积分微分系统，并有一个新的结构，我们通过详细研究类的N-组件的“冷气体”流体动力学减少。我们证明，这些减少代表可积线性退化流体动力学型系统的任意N，这是一个强有力的证据，有利于完整的动力学方程的可积性。我们推导出紧凑的显式表示的黎曼不变量和特征速度的流体动力学减少方面的“冷气体”的组件密度和构造一些具有特殊性质（准周期性，自相似）的精确解。流体动力学对称性，然后推导和研究。所得结果揭示了一类流体动力学型可积系统的连续极限的结构，也与保守可压缩流中湍流运动的描述有关。
We introduce and study a new class of kinetic equations, which arise in the description of nonequilibrium macroscopic dynamics of soliton gases with elastic collisions between solitons. These equations represent nonlinear integro-differential systems and have a novel structure, which we investigate by studying in detail the class of N-component 'cold-gas' hydrodynamic reductions. We prove that these reductions represent integrable linearly degenerate hydrodynamic type systems for arbitrary N which is a strong evidence in favour of integrability of the full kinetic equation. We derive compact explicit representations for the Riemann invariants and characteristic velocities of the hydrodynamic reductions in terms of the 'cold-gas' component densities and construct a number of exact solutions having special properties (quasiperiodic, self-similar). Hydrodynamic symmetries are then derived and investigated. The obtained results shed light on the structure of a continuum limit for a large class of integrable systems of hydrodynamic type and are also relevant to the description of turbulent motion in conservative compressible flows.