标题： 哈密顿量关于孤子气体的运动方程方面 显示英文标题

标题： Hamiltonian aspects of the kinetic equation for soliton gas

摘要： 我们研究密集孤立子气体的积分微分动力学方程的哈密顿方面，该方程作为Whitham方程的热力学极限结果。 在delta函数假设下，动力学方程简化为一个不可对角化的流体动力学类型系统，其矩阵由多个$2\times 2$约当块组成。 我们证明，对于所有标准的双孤立子相互作用核（KdV、sinh-Gordon、硬杆、Lieb-Liniger、DNLS和可分离情况），所得系统具有局部的微分几何型哈密顿结构。 在硬杆情况下，我们表明这些结构的连续极限提供了完整动力学方程的局部多哈密顿表述。 显示英文摘要

摘要： We investigate Hamiltonian aspects of the integro-differential kinetic equation for dense soliton gas which results as a thermodynamic limit of the Whitham equations. Under a delta-functional ansatz, the kinetic equation reduces to a non-diagonalisable system of hydrodynamic type whose matrix consists of several $2\times 2$ Jordan blocks. We demonstrate that the resulting system possesses local Hamiltonian structures of differential-geometric type, for all standard two-soliton interaction kernels (KdV, sinh-Gordon, hard-rod, Lieb-Liniger, DNLS, and separable cases). In the hard-rod case, we show that the continuum limit of these structures provides a local multi-Hamiltonian formulation of the full kinetic equation.