标题： 关于哈里·戴姆方程的双哈密顿理论 显示英文标题

标题： On the Bi-Hamiltonian Theory for the Harry Dym Equation

摘要： 我们描述了Harry Dym方程如何融入Korteweg-de Vries方程和其他孤子方程的双哈密顿形式。这是通过由两个相容的泊松结构构造的某个泊松铅笔实现的。我们得到了Kadomtsev-Petviashivili层次的一个类似物，其约化导致Harry Dym层次。我们将这种系统称为HD-KP层次。然后，我们构建了一个无限的常微分方程组（在无限多个变量中），它与HD-KP层次等价。它的作用类似于Kadomtsev-Petviashivili层次中的中心系统所起的作用。 显示英文摘要

摘要： We describe how the Harry Dym equation fits into the the bi-Hamiltonian formalism for the Korteweg-de Vries equation and other soliton equations. This is achieved by means of a certain Poisson pencil constructed from two compatible Poisson structures. We obtain an analogue of the Kadomtsev-Petviashivili hierarchy whose reduction leads to the Harry Dym hierarchy. We call such system the HD-KP hierarchy. Then, we construct an infinite system of ordinary differential equations (in infinitely many variables) that is equivalent to the HD-KP hierarchy. Its role is analogous to the one played by the Central System for the Kadomtsev-Petviashivili hierarchy.