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

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