The Painlevé tests, B?cklund transformation and bilinear form for the KdV equation with a self-consistent source

摘要

The Painlevé property and B?cklund transformation for the KdV equation with a self-consistent source are presented. By testing the equation, it is shown that the equation has the Painlevé property. In order to further prove its integrality, we give its bilinear form and construct its bilinear B?cklund transformation by the Hirota's bilinear operator. And then the soliton solution of the equation is obtained, based on the proposed bilinear form.