The Painlevé analysis for N=2 super KdV equations

Abstract

The Painlevé analysis of a generic multiparameter N=2 extension of the Korteweg-de Vries equation is presented. Unusual aspects of the analysis, pertaining to the presence of two fermionic fields, are emphasized. For the general class of models considered, we find that the only ones which manifestly pass the test are precisely the four known integrable supersymmetric KdV equations, including the SKdV$_1$ case.