FACTORIZATION OF GELFAND-DICKEY OPERATOR, B?CKLUND-DARBOUX TRANSFORMATION AND SYMMETRY
Gelfand-Dickey算子分解,B?cklund-Darboux变换及对称

Explicit expressions of n B?cklund-Darboux (BD) transformations and corresponding symmetries for generalized KdV (GKdV) equation, were constructed by using factorization of Gelfand-Dickey operator. This extends Lou's recent result about the BD transformations and non-local symmetries for KdV, Kadomtsev-Petviashvilli equations. As a by-product, we also derive a representation of Wronskian determinant for the GKdV solution.