Soliton gas in bidirectional dispersive hydrodynamics
Soliton gas in bidirectional dispersive hydrodynamics
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DOI：
10.1103/physreve.103.042201
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发表时间：
2021-04-02
影响因子：
2.4
通讯作者：
Roberti, Giacomo
中科院分区：
文献类型：
--
作者：
Congy, Thibault;El, Gennady;Roberti, Giacomo
孤立子气体的理论以前已经发展为单向可积色散流体动力学，其中孤立子气体的性质由孤立子之间的超越弹性成对相互作用决定。在本文中，我们将这一理论推广到双向可积欧拉系统中的孤子气体，其中孤子的迎头碰撞和超越碰撞都发生。我们区分两种性质不同类型的双向孤子气体：各向同性气体，其中的位置移动伴随着迎面和超车孤子碰撞具有相同的符号，和各向异性气体，其中的位置移动迎面和超车碰撞具有相反的符号。我们构造两种类型的双向孤子气体的动力学方程，并解决各自的激波管问题的碰撞的两个“单色”孤子光束组成的孤子的振幅和速度大致相同。构造了平均流的由接触间断分隔的不同均匀状态组成的动力学方程的相应弱解。具体例子的双向欧拉孤子气体的散焦非线性薛定谔（NLS）方程和共振NLS方程。共振NLS孤子气体的动力学方程被证明是等效的浅水双向孤子气体的Kaup-Boussinesq方程描述。双向孤立子气体激波管Riemann问题的解析结果与直接数值模拟结果吻合得很好。
The theory of soliton gas had been previously developed for unidirectional integrable dispersive hydrodynamics in which the soliton gas properties are determined by the overtaking elastic pairwise interactions between solitons. In this paper, we extend this theory to soliton gases in bidirectional integrable Eulerian systems where both head-on and overtaking collisions of solitons take place. We distinguish between two qualitatively different types of bidirectional soliton gases: isotropic gases, in which the position shifts accompanying the head-on and overtaking soliton collisions have the same sign, and anisotropic gases, in which the position shifts for head-on and overtaking collisions have opposite signs. We construct kinetic equations for both types of bidirectional soliton gases and solve the respective shock-tube problems for the collision of two "monochromatic" soliton beams consisting of solitons of approximately the same amplitude and velocity. The corresponding weak solutions of the kinetic equations consisting of differing uniform states separated by contact discontinuities for the mean flow are constructed. Concrete examples of bidirectional Eulerian soliton gases for the defocusing nonlinear Schrodinger (NLS) equation and the resonant NLS equation are considered. The kinetic equation of the resonant NLS soliton gas is shown to be equivalent to that of the shallow-water bidirectional soliton gas described by the Kaup-Boussinesq equations. The analytical results for shock-tube Riemann problems for bidirectional soliton gases are shown to be in excellent agreement with direct numerical simulations.