标题： 2+1维双曲型哈密顿系统色散变形 显示英文标题

标题： Dispersive deformations of Hamiltonian systems of hydrodynamic type in 2+1 dimensions

摘要： 我们发展了一种2+1维哈密顿流体动力学型系统的可积色散扰动理论，遵循杜布罗文及其合作者在1+1维中提出的方案。 我们的结果表明，多维情况要严格得多，一般的哈密顿量是不可扰动的。 作为说明，我们讨论了一类双组分哈密顿系统，确立了第一阶扰动的平凡性，并对具有非平凡二阶扰动的哈密顿量进行了分类。 显示英文摘要

摘要： We develop a theory of integrable dispersive deformations of 2+1 dimensional Hamiltonian systems of hydrodynamic type following the scheme proposed by Dubrovin and his collaborators in 1+1 dimensions. Our results show that the multi-dimensional situation is far more rigid, and generic Hamiltonians are not deformable. As an illustration we discuss a particular class of two-component Hamiltonian systems, establishing the triviality of first order deformations and classifying Hamiltonians possessing nontrivial deformations of the second order.