On a fermionic extension of [formula omitted] equation.

A fermionic extension of K (− 1 , − 2) equation, alias a super K (− 1 , − 2) equation, proposed by Tempesta et al. (2003), is converted to the N = 1 supersymmetric Korteweg–de Vries equation via invertible transformations involving both independent and dependent variables. As implementation of this intimate connection, some integrable properties are established for the fermionic extension of K (− 1 , − 2) equation, including a linear spectral problem in terms of 3 × 3 matrices, a Bäcklund transformation, a nonlinear superposition formula, infinitely many conservation laws, as well as its bi-Hamiltonian formulation. • A fermionic extension of K (− 1 , − 2) equation is changed to the N = 1 SUSY KdV equation. • A Bäcklund transformation and a nonlinear superposition formula are constructed. • Infinitely many conservation laws and the bi-Hamiltonian structure are established. [ABSTRACT FROM AUTHOR]