A new Backlund transformation and multi-soliton solutions to the KdV equation with general variable coefficients

A new Backlund transformation (BT) to the KdV equation with general variable coefficients is derived by using the homogeneous balance principle (HBP) if the coefficients to the equation are linearly dependent. Based on the BT in which there is only one quadratic homogeneity equation to be solved, generally speaking, the multi-soliton solutions with a variable propagating speed to the equation can be completely obtained by using the epsilon -expansion method. As an illustrative example, the 2-soliton solution is given and discussed in detail. (C) 2001 Published by Elsevier Science B.V.