Bilinear Approach to N=2 Supersymmetric KdV equations

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.