On a direct procedure for the quasi-periodic wave solutions of the supersymmetric Itoʹs equation

A direct scheme is proposed to explicitly construct quasi-periodic wave solutions of the supersymmetric Itoʹs equation in superspace. This scheme is based on super Hirota bilinear formalism and a Riemann theta function formula. The relations between the periodic wave solutions and the well-known soliton solutions are rigorously established. Some new phenomena on super quasi-periodic waves are observed. For instance, there is an interesting influencing band occurred among the super quasi-periodic waves under the presence of the Grassmann variable. The super quasi-periodic waves are symmetric about the band but collapse along with the band.