Supersymmetric Extensions of the Harry Dym Hierarchy

Abstract

We study the supersymmetric extensions of the Harry Dym hierarchy of equations. We obtain the susy-B extension, the doubly susy-B extension as well as the N=1 and the N=2 supersymmetric extensions for this system. The N=2 supersymmetric extension is particularly interesting, since it leads to new classical integrable systems in the bosonic limit. We prove the integrability of these systems through the bi-Hamiltonian formulation of integrable models and through the Lax description. We also discuss the supersymmetric extension of the Hunter-Zheng equation which belongs to the Harry Dym hierarchy of equations.

15 pages, Latex file

References in corpus (1)

• On the Nonlocal Equations and Nonlocal Charges Associated with the Harry Dym Hierarchy

Cited by in corpus (11)

• Classical R-matrix theory for bi-Hamiltonian field systems
• Supersymmetric Reciprocal Transformation and Its Applications
• The Generalized Harry Dym Equation
• Euler Equations Related to the Generalized Neveu-Schwarz Algebra
• A non-standard Lax formulation of the Harry Dym hierarchy and its supersymmetric extension
• The Even and Odd Supersymmetric Hunter - Saxton and Liouville Equations
• Deformed Harry Dym and Hunter-Zheng Equations
• The transformations between N=2 supersymmetric KdV and HD equations
• Transformation of a generalized Harry Dym equation into the Hirota--Satsuma system
• On bosonic limits of two recent supersymmetric extensions of the Harry Dym hierarchy
• On a set of Grassmann-valued extensions of systems of ordinary differential equations