Integrable discretizations and soliton solution of KdV and mKdV equations

A method of integrable discretizations for soliton equations is presented, which is based on the bilinear formalism. Taking the KdV equation and mKdV equation for example, we discretize the corresponding bilinear equations through properly replacing Hirota operator by the hyperbolic operator. We also get the soliton solutions of these discrete equations by Hirota’s bilinear method.