Fermionic extension of the scalar Born-Infeld equation and its relation to the supersymmetric Chaplygin gas

In this article, we present a fermionic extension of the scalar Born-Infeld equation, which has been derived from the Nambu-Goto superstring action in (2+1) dimensions through the Cartesian parameterization. It is demonstrated that in the relativistic limit where c \to \infty, the fermionic Born-Infeld model reduces to the supersymmetric Chaplygin gas model in one spatial dimension. However, the supersymmetry itself is not preserved.