HIROTA BILINEAR FORM FOR THE SUPER-KdV HIERARCHY

Abstract

The integrability of the super-KdV hierarchy suggests that it can be written in Hirota bilinear form as the group orbit equation for some infinite-dimensional Lie algebra. We show how the first few equations in the hierarchy can be written in Hirota bilinear form. We also conjecture a bilinear expression for the whole super-KdV hierarchy and check it to reasonably high orders. A by-product is an expression for the ordinary KdV hierarchy which provides an alternative to the ones obtained by Date et al. and Kac and Wakimoto.