Super extension of Bell polynomials with applications to supersymmetric equations

In this paper, we generalize classical Bell polynomials into super version, which are found to be effective in systematically constructing super bilinear representation, bilinear Bäcklund transformation, Lax pair, and infinite conservation laws of supersymmetric equations. We take \documentclass[12pt]{minimal}\begin{document}$\mathcal{N}=1$\end{document} N = 1 supersymmetric KdV equation and \documentclass[12pt]{minimal}\begin{document}$\mathcal{N}=2$\end{document} N = 2 supersymmetric sine-Gordon equation to illustrate this procedure.