Extension of the bilinear formalism to supersymmetric KdV-type equations

Extending the gauge-invariance principle for tau functions of the standard bilinear formalism to the supersymmetric case, we define N = 1 supersymmetr ic Hirota operators. Using them, we bilinearize SUSY KdV-type equations (Kd V, Sawada-Kotera-Ramani). The supersoliton solutions and extension to SUSY sine-Gordon are also discussed. It is shown that the Lax-integrable SUSY Kd V of the Mathieu equation does not possess an N-supersoliton solution for N greater than or equal to 3 for arbitrary parameters. The N-supersoliton so lution only exists for a particular choice of parameters. AMS classificatio n scheme numbers: 37K10, 35Q51.