The Painlev\'e analysis for N=2 super KdV equations

TL;DR

This paper applies Painlevé analysis to a class of N=2 super KdV equations, highlighting unique features due to fermionic fields and confirming integrability of known models.

Contribution

It extends Painlevé analysis to multiparameter N=2 super KdV equations, identifying conditions for integrability related to fermionic field presence.

Findings

Only four known supersymmetric KdV equations pass the Painlevé test.

Unusual aspects arise from the presence of two fermionic fields.

The analysis confirms integrability of specific N=2 super KdV models.

Abstract

The Painlev\'e 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.