Soliton solutions of the Korteweg de Vries and the Kadomtsev-Petviashvili equations: the Wronskian technique

Abstract

Abstract The well known soliton solutions of the Kadomtsev-Petviashvili equations are written in terms of determinants of Wronskian form. By using this compact representation together with the Hirota bilinear form of the equations, it is demonstrated by elementary algebraic methods that the N-soliton solution satisfies the evolution equation and the N and N + 1-soliton solutions satisfy the associated Bäcklund transformation. The relation of these results to the eigensolutions of the inverse scattering method and to the more usual representation of the N-soliton solution is also given.