A Supersymmetric Ito's Equation and its Soliton Solutions

Abstract

In this paper, we propose a supersymmetric Ito equation (sIto) and calculate its one-, two-, and three-soliton solutions within the framework of Hirota's bilinear method. We also construct the Lax representation, Bäcklund transformation and nonlinear superposition formula for this supersymmetric equation.