Bäcklund transformation and multi-soliton solutions for the discrete Korteweg–de Vries equation

Abstract

In this paper, a discrete Korteweg–de Vries equation for an LC network consisting of the voltage-dependent capacitors and current-dependent inductors is investigated by symbolic computation. Binary Bell polynomials are applied to the discrete Korteweg–de Vries equation which is reduced to the corresponding bilinear form directly rather than transformed into its fourlinear one first. Simultaneously, the dependent variable transformation is acquired through the deriving procedures. Bäcklund transformation of the dKdV equation is derived with the introduced mixing variables instead of the exchange formulae. Solitonic propagation and interaction in the electrical circuit are illustrated and analyzed.