On a fermionic extension of [formula omitted] equation

Abstract

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.