Bilinear approach to Kuperschmidt super-KdV type equations

Hirota bilinear form and soliton solutions for the super-KdV (Korteweg–de Vries) equation of Kuperschmidt (Kuper–KdV) are given. It is shown that even though the collision of supersolitons is more complicated than in the case of the supersymmetric KdV equation of Manin–Radul, the asymptotic effect of the interaction is simpler. As a physical application it is shown that the well-known FPU problem, having a phonon-mediated interaction of some internal degrees of freedom expressed through Grassmann fields, transforms to the Kuper–KdV equation in a multiple-scale approach. (paper)