Bilinear Backlund transformation for the KdV equation with a source

A bilinear Backlund transformation for the KdV equation with a source is obtained by using the bilinear transformation method. Superposition formulae for solutions are then constructed which satisfy Bianchi's exchange property and it is shown that they have a simple structure when they are written in the bilinear forms. The inverse scattering transform for the equation is also derived from the Backlund transformation.

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