非线性偏微分方程Miura，Bäcklund和达布变换的统一解法
Unified approach to Miura, Bäcklund and Darboux transformations for nonlinear partial differential equations
摘要：
本文试图介绍和讨论在一定长度的奇异流形方法。该方法基于Painlevé性质，系统地用作一种工具，用于以统一的方式获得几乎所有与非线性偏微分方程相关的问题的明确答案：拉克斯对、Miura、Bäcklund或达布变换以及$τ$ -函数。除了介绍方法的基础知识外，我们还通过将其应用于$(1+1)$维中的四个方程来验证这种方法。其中两个与其他两个通过三浦变换，也来自使用奇异流形方法。
英文摘要：
This paper is an attempt to present and discuss at some length the Singular Manifold Method. This Method is based upon the Painlevé Property systematically used as a tool for obtaining clear cut answers to almost all the questions related with Nonlinear Partial Differential Equations: Lax pairs, Miura, Bäcklund or Darboux Transformations as well as $τ$-functions, in a unified way. Besides to present the basics of the Method we exemplify this approach by applying it to four equations in $(1+1)$-dimensions. Two of them are related with the other two through Miura transformations that are also derived by using the Singular Manifold Method.
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