摘要：This paper begins with a brief review of the history of the Painlevé property. The Painlevé test is applied to two non linear partial differential equations (the Tu equation, and an extended mKdV equation) which have not been tested in this way before, and it is proved that these two equations possess the Painlevé property. The Painlevé analysis also is used to determine a Bäcklund transformation and the bilinear form of the Tu equation. A similarity reduction for this equation is found by means of the Clarkson-Kruskal method.
其他摘要：This paper begins with a brief review of the history of the Painlevé property. The Painlevé test is applied to two non linear partial differential equations (the Tu equation, and an extended mKdV equation) which have not been tested in this way before, and it is proved that these two equations possess the Painlevé property. The Painlevé analysis also is used to determine a Bäcklund transformation and the bilinear form of the Tu equation. A similarity reduction for this equation is found by means of the Clarkson-Kruskal method.
