REDUCE

16.66 SSTOOLS: Computations with supersymmetric algebraic and differential expressions

Authors: Thomas Wolf and Eberhard Schruefer

16.66.1 Overview

A detailed description is available through the online tutorial
https://lie.ac.brocku.ca/crack/susy/. An essentially equivalent description is available after loading SSTOOLS and issuing the command sshelp()$. The correct functioning of all procedures is tested through reading in and running sstools.tst. This test also illustrates the commutator rules for products of the different fields and their derivatives with respect to besonic and fermionic variables.

The topics in the tutorial and in sshelp()$ are:

Purpose
Interactive Session
Loading Files
Notation
Initializations
The command coeffn
The procedure SSym
The procedure SSConL
The procedure FindSSWeights
The procedure Linearize
The procedure GenSSPoly
The procedure ToCoo
The procedure ToField
Discovery of recursion operators
Verification of symmetries

Bibliography

[1]   Hussin, V., Kiselev, A.V., Krutov, A.O., Wolf, T.: N=2 Supersymmetric a=4 - Korteweg-de Vries hierarchy derived via Gardner’s deformation of Kaup-Bousinesq equation, J. Math. Phys. 51, 083507 (2010); doi:10.1063/1.3447731 (19 pages) link, pdf file

[2]   Kiselev, A. and Wolf, T.: Supersymmetric Representations and Integrable Super-Extensions of the Burgers and Bussinesq Equations, SIGMA, Vol. 2 (2006), Paper 030, 19 pages (arXiv math-ph/0511071). ps file, pdf file

[3]   Kiselev, A. and Wolf, T.: On weakly non-local, nilpotent, and super-recursion operators for N=1 homogeneous super-equations, Proc. Int. Workshop “Supersymmetries and Quantum Symmetries” (SQS’05), Dubna, July 24–31, 2005, JINR, p. 231–237. (arXiv nlin.SI/0511056) http://theor.jinr.ru/ sqs05/SQS05.pdf dvi file, ps file,

[4]   Kiselev, A. and Wolf, T.: Classification of integrable super-equations by the SsTools environment, Comp Phys Comm, Vol. 177, no. 3 (2007) p 315-328 (and on arXiv: nlin.SI/0609065). dvi file, ps file, pdf file

[5]   I. S. Krasil’shchik, P. H. M. Kersten, Symmetries and recursion operators for classical and supersymmetric differential equations, Kluwer Acad. Publ., Dordrecht etc, (2000)