Painlevé integrability of the supersymmetric Ito equation*

A supersymmetric version of the Ito equation is proposed by extending the independent and dependent variables for the classic Ito equation. To investigate the integrability of the N = 1 supersymmetric Ito (sIto) equation, a singularity structure analysis for this system is carried out. Through a detailed analysis in two cases by using Kruskal’s simplified method, the sIto system is found to pass the Painlevé test, and thus is Painlevé integrable.