New solution of the $\mathcal{N}=2$ Supersymmetric KdV equation via Hirota methods

TL;DR

This paper develops a Hirota formalism for the $ abla$2 supersymmetric KdV equation with $a=-2$, deriving its bilinear form and constructing multisoliton and rational solutions.

Contribution

It introduces the first bilinear form for the $SKdV_{a=-2}$ equation and constructs explicit multisoliton and rational solutions.

Findings

First bilinear form of the $SKdV_{a=-2}$ equation

Explicit multisoliton solutions

Rational similarity solutions

Abstract

We consider the resolution of the $\mathcal{N}=2$ supersymmetric KdV equation with $a=-2$ ($SKdV_{a=-2}$) from the Hirota formalism. For the first time, a bilinear form of the $SKdV_{a=-2}$ equation is constructed. We construct multisoliton solutions and rational similarity solutions.