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In this paper, we construct and investigate two supersymmetric versions ofthe Fokas-Gel'fand formula for the immersion of 2D surfaces associated with asupersymmetric integrable system. The first version involves an infinitesimaldeformation of the zero-curvature condition and the linear spectral problemassociated with this system. This deformation leads the surfaces to berepresented in terms of a bosonic supermatrix immersed in a Lie superalgebra.The second supersymmetric version is obtained by using a fermionic parameterdeformation to construct surfaces expressed in terms of a fermionic supermatriximmersed in a Lie superalgebra. For both extensions, we provide a geometricalcharacterization of deformed surfaces using the super Killing form as an innerproduct and a super moving frame formalism. The theoretical results are appliedto the supersymmetric sine-Gordon equation in order to construct super solitonsurfaces associated with five different symmetries. We find integrated forms ofthese surfaces which represent constant Gaussian curvature surfaces andnonlinear Weingarten-type surfaces.

Supersymmetric versions of the Fokas-Gel'fand formula for immersion