NONCLASSICAL SYMMETRIES AND THE SINGULAR MANIFOLD METHOD - THEORY AND 6 EXAMPLES

作者：ESTEVEZ PG^*; GORDOA PR

来源：Studies in Applied Mathematics, 1995, 95(1): 73-113.

In this paper we discuss a new approach to the relationship between integrability and symmetries of a nonlinear partial differential equation. The method is based heavily on ideas using both the Painleve property and the singular manifold analysis, which is of outstanding importance in understanding the concept of integrability of a given partial differential equation. In our examples we show that the solutions of the singular manifold possess Lie point symmetries that correspond precisely to the so-called nonclassical symmetries. We also point out the connection between the singular manifold method and the direct method of Clarkson and Kruskal. Here the singular manifold is a function of its reduced variable. Although the Painleve property plays an essential role in our approach, our method also holds for equations exhibiting only the conditional Painleve property, We offer six full examples of how our method works for the six equations, which we believe cover all possible cases.

• 出版日期1995-7