Bilinear approach to Kuperschmidt super-KdV type equations

TL;DR

This paper derives Hirota bilinear forms and soliton solutions for the super-KdV Kuperschmidt equation, revealing simpler asymptotic interactions despite complex collisions, and connects it to physical phonon interactions in the FPU problem.

Contribution

It introduces a bilinear approach and soliton solutions for the Kuperschmidt super-KdV equation, expanding understanding of supersoliton interactions and their physical relevance.

Findings

Soliton solutions for super-KdV Kuperschmidt equation are constructed.

Asymptotic interactions of supersolitons are simpler than in supersymmetric KdV.

Connection established between Kuperschmidt super-KdV and FPU phonon interactions.

Abstract

Hirota bilinear form and soliton solutions for super-KdV of Kuperschmidt (Kuper-KdV) are given. It is shown that even though the collision of supersolitons is more complicated than in the case of supersymmetric KdV 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, goes to the Kuper-KdV equation in a multiple-scale approach.