The Even and Odd Supersymmetric Hunter - Saxton and Liouville Equations

TL;DR

This paper introduces two distinct supersymmetric extensions of the Hunter-Saxton equation, one known and one new, and demonstrates their reciprocal transformations to supersymmetric Liouville equations, enriching the understanding of supersymmetric integrable systems.

Contribution

It presents a novel odd supersymmetric Hunter-Saxton equation and explores its connection to supersymmetric Liouville equations through reciprocal transformations.

Findings

One extension yields the known even supersymmetric Hunter-Saxton equation.

The second extension is a new odd supersymmetric Hunter-Saxton equation.

Both are transformed into different supersymmetric Liouville equations.

Abstract

It is shown that two different supersymmetric extensions of the Harry Dym equation lead to two different negative hierarchies of the supersymmetric integrable equations. While the first one yields the known even supersymmetric Hunter - Saxton equation, the second one is a new odd supersymmetric Hunter - Saxton equation. It is further proved that these two supersymmetric extensions of the Hunter - Saxton equation are reciprocally transformed to two different supersymmetric extensions of the Liouville equation.