<b><i>N</i></b>soliton solutions to the Bogoyavlenskii-Schiff equation and a quest for the soliton solution in (3 1) dimensions

Abstract

We study the integrable systems in higher dimensions which can be written by the trilinear form instead of by the Hirota's bilinear form. We explicitly discuss the Bogoyavlenskii-Schiff equation in (2 + 1) dimensions. Its analytical proof of multisoliton solution and a new feature are given. Being guided by the strong symmetry, we also propose a new equation in (3 + 1) dimensions.