2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79822Extending the gauge-invariance principle for $τ$ functions of the standard bilinear formalism to the supersymmetric case, we define ${\cal N}=1$ supersymmetric Hirota bilinear operators. Using them we bilinearize supersymmetric nonlinear evolution equations. The super-soliton solutions are discussed. As a quite strange paradox it is shown that the Lax integrable supersymmetric KdV of Manin-Radul-Mathieu equation does not possesses N super-soliton solution for $N\geq 3$ for arbitrary parameters. Only for a particular choice of them the N super-soliton solution exists.22 pages, no figures, to appear in NonlinearityExactly Solvable and Integrable SystemsMathematical Physicstext