Discrete and ultradiscrete Bäcklund transformation for KdV equation.

The Bäcklund transformation for the discrete Korteweg-de Vries equation is introduced in the bilinear form. The superposition formula is also derived from the transformation. An ultradiscrete analogue of the transformation is presented by means of the ultradiscretization technique. This analogue gives the Bäcklund transformation for the box and ball system. The ultradiscrete soliton solutions for the system are also discussed with explicit examples. [ABSTRACT FROM AUTHOR]