标题： 引力孤立子与单值变换方法求解爱因斯坦方程的可积约化问题 显示英文标题

标题： Gravitational Solitons and Monodromy Transform Approach to Solution of Integrable Reductions of Einstein Equations

摘要： 本文在所谓的“单值变换方法”的背景下，考虑了具有二维阿贝尔等距群的真空爱因斯坦方程解空间中著名的Belinskii和Zakharov孤子生成变换。这种方法为研究爱因斯坦方程的各种可积时空对称约化提供了一般的基础。 类似于已知谱变换中使用的散射数据，在这种方法中，单值数据完全表征了约化爱因斯坦方程的任意解，且解的许多物理和几何性质可以直接用相应单值数据函数的谱平面上的解析结构来表达。 Belinskii和Zakharov的真空孤子生成变换可以以显式形式表示（无需指定背景解），即对应单值数据函数的简单（线性分式）变换，其系数为谱参数的多项式。这使得可以在计算解的所有分量之前或没有计算的情况下确定生成孤子解的许多物理参数。 文中还给出了电真空孤子生成变换的类似描述。 显示英文摘要

摘要： In this paper the well known Belinskii and Zakharov soliton generating transformations of the solution space of vacuum Einstein equations with two-dimensional Abelian groups of isometries are considered in the context of the so called "monodromy transform approach", which provides some general base for the study of various integrable space - time symmetry reductions of Einstein equations. Similarly to the scattering data used in the known spectral transform, in this approach the monodromy data for solution of associated linear system characterize completely any solution of the reduced Einstein equations, and many physical and geometrical properties of the solutions can be expressed directly in terms of the analytical structure on the spectral plane of the corresponding monodromy data functions. The Belinskii and Zakharov vacuum soliton generating transformations can be expressed in explicit form (without specification of the background solution) as simple (linear-fractional) transformations of the corresponding monodromy data functions with coefficients, polynomial in spectral parameter. This allows to determine many physical parameters of the generating soliton solutions without (or before) calculation of all components of the solutions. The similar characterization for electrovacuum soliton generating transformations is also presented.