Summary: Extending the gauge-invariance principle for \(\tau\)-functions of the standard bilinear formalism to the supersymmetric case, we define \(N=1\) supersymmetric Hirota operators. Using them, we bilinearize SUSY KdV-type equations (KdV, Sawada-Kotera-Ramani). The supersoliton solutions and extension to SUSY sine-Gordon are also discussed. It is shown that the Lax-integrable SUSY KdV of the Mathieu equation does not possess an \(N\)-supersoliton solution for \(N\geq 3\) for arbitrary parameters.The \(N\)-supersoliton solution only exists for a particular choice of parameters.