WHEN THE SUPERSYMMETRY IS NOT ENOUGH: THE PARASUPERSYMMETRIC ALGEBRAS OF THE BOUSSINESQ EQUATIONS

Abstract

In this article we look at a conundrum that the Boussinesq-type equations pose for mathematicians allowing a Miura-type transformation while at the same time exhibiting no trace of a supersymmetric structure. We demonstrate that this riddle should be unraveled by dropping the standard supersymmetric approach in favor of its generalization: the “parasupersymmetry”.

Keywords

• supersymmetry
• Boussinesq equation