Soliton gas in integrable dispersive hydrodynamics
Soliton gas in integrable dispersive hydrodynamics
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DOI：
10.1088/1742-5468/ac0f6d
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发表时间：
2021-11-01
影响因子：
2.4
通讯作者：
El, Gennady A.
中科院分区：
文献类型：
--
作者：
El, Gennady A.
我们回顾了可积色散流体动力系统中孤子气体的谱理论。我们首先提出了一种唯象方法，该方法基于对成对孤子碰撞中相移的考虑，并得出非平衡孤子气体的动力学方程。然后，提出了更详细的理论，其中孤子气体动力学通过 Korteweg-de Vries 的调制有限间隙谱解的热力学类型极限和聚焦非线性薛定谔 (NLS) 方程进行建模。对于聚焦 NLS 方程，引入了与自发调制不稳定和异常波形成现象相关的孤子凝聚和呼吸气体的概念。讨论了孤子气体动力学方程的可积性质，提出了一些物理相关的解，并与色散流体动力系统的直接数值模拟进行了比较。
We review the spectral theory of soliton gases in integrable dispersive hydrodynamic systems. We first present a phenomenological approach based on the consideration of phase shifts in pairwise soliton collisions and leading to the kinetic equation for a non-equilibrium soliton gas. Then, a more detailed theory is presented in which soliton gas dynamics are modelled by a thermodynamic type limit of modulated finite-gap spectral solutions of the Korteweg-de Vries and the focusing nonlinear Schrodinger (NLS) equations. For the focusing NLS equation the notions of soliton condensate and breather gas are introduced that are related to the phenomena of spontaneous modulational instability and the rogue wave formation. The integrability properties of the kinetic equation for soliton gas are discussed and some physically relevant solutions are presented and compared with direct numerical simulations of dispersive hydrodynamic systems.