Links between symmetry reduction and Hirota methods of the N=2 susy KdV equation

TL;DR

This paper explores the connection between symmetry reduction and Hirota methods for solving the N=2 supersymmetric KdV equation, deriving new solutions and establishing links between the two approaches.

Contribution

It constructs a bilinear form of the N=2 supersymmetric KdV equation and links the symmetry reduction and Hirota methods, leading to new solutions.

Findings

Established links between symmetry reduction and Hirota methods.

Constructed a bilinear form of the N=2 supersymmetric KdV equation.

Obtained new solutions from both approaches.

Abstract

We consider the resolution of the N=2 supersymmetric KdV equation with a=-2 (SKdV_{a=-2}) from two approaches, the group invariant method (or symmetry reduction) and the Hirota formalism. A bilinear form of the SKdV_{a=-2} equation is constructed. Links between the two methods are established and new solutions are obtained from both approaches.