Title: Bilinear approach to the supersymmetric Gardner equation,
Abstract: We study a supersymmetric version of the Gardner equation (both focusing and
defocusing) using the superbilinear formalism. This equation is new and cannot
be obtained from supersymmetric modified Korteweg-de Vries equation with a
nonzero boundary condition. We construct supersymmetric solitons and then by
passing to the long-wave limit in the focusing case obtain rational nonsingular
solutions. We also discuss the supersymmetric version of the defocusing
equation and the dynamics of its solutions.