Quasilinear systems of Jordan block type and the mKP hierarchy

Jordan块型抛物方程组的拟线性微分约束

Quasilinear differential constraints for parabolic systems of Jordan-block type

本研究针对Jordan块型抛物方程组，证明线性退化是其容许相容拟线性微分约束的必要条件，对2×2方程组该条件充分且等价于哈密顿性，还给出了两类相关抛物系统的显式解。

Jordan 块型哈密顿系统：孤子气体动力学方程的 delta 函数约化

Hamiltonian systems of Jordan block type: delta-functional reductions of the kinetic equation for soliton gas

本文证明线性退化是 Jordan 块型拟线性系统存在一阶哈密顿结构的必要条件，并建立了稠密孤子气体动力学方程 delta 函数约化的多哈密顿表述，涵盖多种可积模型。

Kinetic equation for soliton gas: integrable reductions

Macroscopic dynamics of soliton gases can be analytically described by the thermodynamic limit of the Whitham equations, yielding an integro-differential kinetic equation for the density of states. Under a delta-functional ansatz, the kinetic equation for soliton gas reduces to a non-diagonalisable system of hydrodynamic type whose matrix consists of several 2x2 Jordan blocks. Here we demonstrate the integrability of this system by showing that it possesses a hierarchy of commuting hydrodynamic flows and can be solved by an extension of the generalised hodograph method. Our approach is a gener…