A bi-Hamiltonian supersymmetric geodesic equation
Jonatan Lenells
TL;DR
This paper introduces a supersymmetric extension of the Hunter-Saxton equation, demonstrating its bi-Hamiltonian structure and geometric interpretation as a geodesic equation on a superdiffeomorphism space.
Contribution
It constructs a novel supersymmetric Hunter-Saxton equation with a bi-Hamiltonian structure and geometric formulation, expanding the understanding of supersymmetric integrable systems.
Findings
The supersymmetric Hunter-Saxton equation has a bi-Hamiltonian structure.
It is geometrically realized as a geodesic flow on a superdiffeomorphism group.
The work links supersymmetry, geometry, and integrable PDEs.
Abstract
A supersymmetric extension of the Hunter-Saxton equation is constructed. We present its bi-Hamiltonian structure and show that it arises geometrically as a geodesic equation on the space of superdiffeomorphisms of the circle that leave a point fixed endowed with a right-invariant metric.
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