扭量空间中的孤子与有理曲线的容许族
Solitons and admissible families of rational curves in twistor spaces
摘要：
扭量结构可以用来分析和求解一类广泛的可积系统。在这篇文章中，我们表示的标准扭量结构的概念，允许家庭的有理曲线在一定的扭量空间。这样的族的例子可以通过使用代数几何的标准运算作为有理曲线的简单族的子族来获得。通过几个例子的检验，我们证明了这种构造是数学物理中各种可积微分方程的许多最重要的孤子解和代数解的构造基础。这是作为一个主要的证据，在某种意义上说，所有的孤子类的解决方案应该以这种方式建设。
英文摘要：
It is well known that twistor constructions can be used to analyse and to obtain solutions to a wide class of integrable systems. In this article we express the standard twistor constructions in terms of the concept of an admissible family of rational curves in certain twistor spaces. Examples of of such families can be obtained as subfamilies of a simple family of rational curves using standard operations of algebraic geometry. By examination of several examples, we give evidence that this construction is the basis of the construction of many of the most important solitonic and algebraic solutions to various integrable differential equations of mathematical physics. This is presented as evidence for a principal that, in some sense, all soliton-like solutions should be constructable in this way.
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