B?CKLUND TRANSFORMATION, LAX PAIRS, SYMMETRIES AND EXACT SOLUTIONS FOR VARIABLE COEFFICIENT KdV EQUATION

The homogeneous balance method is extended to seek for B\ddot\rm acklund transformation, Lax pairs, non-local symmetries of variable coefficient KdV equation (VCKdVE). Then based on the B\ddot\rm acklund transformation and general solutions of a fourth-order nonlinear ordinary differential equation, five kinds of exact solutions of VCKdVE are derived. The soliton-like solution also belongs to these solutions.