# Supersymmetry for integrable hierarchies on loop superalgebras

@article{Aratyn2005SupersymmetryFI, title={Supersymmetry for integrable hierarchies on loop superalgebras}, author={Henrik Aratyn and J F Gomes and G. M. de Castro and M. B. Silka and Abraham Hirsz Zimerman}, journal={Journal of Physics A}, year={2005}, volume={38}, pages={9341-9357} }

An algebraic approach is employed to formulate N = 2 supersymmetry transformations in the context of integrable systems based on loop superalgebras , with homogeneous gradation. We work with extended integrable hierarchies, which contain supersymmetric AKNS and Lund–Regge sectors. We derive the one-soliton solution for p = 1 which solves positive and negative evolution equations of the N = 2 supersymmetric model.

## 6 Citations

### A class of mixed integrable models

- Physics
- 2009

The algebraic structure of the integrable mixed mKdV/sinh-Gordon model is discussed and extended to the AKNS/Lund–Regge model and to its corresponding supersymmetric versions. The integrability of…

### Supersymmetry of Affine Toda Models as Fermionic Flows of the Extended mKdV Hierarchy

- Physics
- 2009

We present an algebraic derivation of the supersymmetry flow transformations for the relativistic sector of the extended mKdV hierarchy. The deduction relies in the introduction of Fermionic Lax…

### Supersymmetry of Affine Toda Models as Fermionic Symmetry Flows of the Extended mKdV Hierarchy

- Physics
- 2010

We couple two copies of the supersymmetric mKdV hierarchy by means of the algebraic dressing technique. This allows to deduce the whole set of (N,N) supersymmetry transformations of the relativistic…

### N = 2 Supersymmetric Unconstrained Matrix GNLS Hierarchies are Consistent

- Mathematics
- 2007

We develop a pseudo-differential approach to the N = 2 supersymmetric unconstrained matrix (k|n, m)-generalized nonlinear Schrödinger hierarchies and prove consistency of the corresponding Lax-pair…

### Hamiltonian and Super-Hamiltonian Extensions Related to Broer-Kaup-Kupershmidt System

- Mathematics
- 2010

Based on the Lie algebra A1, the integrable Broer-Kaup-Kupershmidt (BKK) system is revisited. The bi-Hamiltonian structure is constructed by the trace identity. Two extensions of the Lie algebra A1…

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