Bilinear Approach to N=2 Supersymmetric KdV equations

TL;DR

This paper develops bilinear formulations and constructs solutions for N=2 supersymmetric KdV equations, including a Bäcklund transformation for the a=1 case, advancing methods for solving these integrable systems.

Contribution

It introduces bilinear forms and solutions for two N=2 supersymmetric KdV equations, including a novel Bäcklund transformation for the a=1 case.

Findings

Bilinear formulations for N=2, a=4 and a=1 supersymmetric KdV equations

Construction of particular solutions for both equations

Introduction of a bilinear Bäcklund transformation for the a=1 case

Abstract

The N=2 supersymmetric KdV equations are studied within the framework of Hirota's bilinear method. For two such equations, namely $N=2, a=4$ and $N=2, a=1$ supersymmetric KdV equations, we obtain the corresponding bilinear formulations. Using them, we construct particular solutions for both cases. In particular, a bilinear B\"{a}cklund transformation is given for the $N=2, a=1$ supersymmetric KdV equation.