Deformations of N=2 super-conformal algebra and supersymmetric two-component Camassa-Holm equation

TL;DR

This paper explores the connection between deformations of N=2 superconformal algebra and a supersymmetric two-component Camassa-Holm equation, revealing new algebraic structures and conserved quantities in the hierarchy.

Contribution

It introduces a novel link between superconformal algebra deformations and a supersymmetric integrable PDE, including the derivation of compatible brackets and conserved Hamiltonians.

Findings

Deformation of superconformal algebra yields two compatible brackets.

One bracket admits a momentum operator linked to Sobolev norm.

A hierarchy of conserved Hamiltonians is generated via Lenard relations.

Abstract

This paper is concerned with a link between central extensions of N=2 superconformal algebra and a supersymmetric two-component generalization of the Camassa--Holm equation. Deformations of superconformal algebra give rise to two compatible bracket structures. One of the bracket structures is derived from the central extension and admits a momentum operator which agrees with the Sobolev norm of a coadjoint orbit element. The momentum operator induces via Lenard relations a chain of conserved hamiltonians of the resulting supersymmetric Camassa-Holm hierarchy.