Nonlinear Partial Difference Equations. I. A Difference Analogue of the Korteweg-de Vries Equation

A systematic method for isolating certain nonlinear partial difference equations that exhibit solitons is proposed. A nonlinear partial difference equation which approximates the Korteweg-de Vries equation in the weakly nonlinear and continuum limit, is obtained. N-soliton solutions, the Bäcklund transformation and the inverse scattering transform for this equation are presented.