Connection Between Painlevé Property and Hirota’sBilinearization

Abstract

The main goal of this paper is to consider the connection between Hirota’smethod and Painlevé property based on a result obtained by Gibbon et al. in 1985 toKdV equation. Our contribution is a modification to their work, so that Bäcklundtransformation derived from Painlevé property can be obtained in a systematic wayfrom Hirota’s bilinear form.We find that the modified procedure can be applied to many equations. Amongthese are Boussinesq (B), KP and CDG equations.Also in this paper, some useful properties for the bilinear operators are derived toprove our main results