Multisoliton solution and super-bilinear form of lattice supersymmetric KdV equation

TL;DR

This paper develops multisoliton solutions and bilinear forms for discrete supersymmetric KdV equations, revealing new integrable models with fermionic interactions and their continuum limits.

Contribution

It introduces a new integrable semidiscrete and fully discrete supersymmetric KdV model with a simplified bilinear form and complex fermionic dressing.

Findings

Multisoliton solutions for discrete supersymmetric KdV are constructed.

A new integrable discrete supersymmetric KdV with simpler bilinear form is proposed.

Continuum limit of the discrete models recovers known supersymmetric KdV behavior.

Abstract

Hirota bilinear form and multisoliton solution for semidiscrete and fully discrete (difference-difference) versions of supersymmetric KdV equation found by Xue, Levi and Liu [1] is presented. The solitonic interaction term displays a fermionic dressing factor as in the continuous supersymmetric case. Using bilinear equations it is shown also that there can be constructed a new integrable semidiscrete (and fully discrete) version of supersymmetric KdV which has simpler bilinear form but more complicated interaction dressing. Its continuum limit is also computed.