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Manuscript Title: Classification of integrable super-systems using the SsTools environment
Authors: A. V. Kiselev, T. Wolf
Program title: SsTools
Catalogue identifier: ADYY_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 177(2007)315
Programming language: REDUCE 3.7, REDUCE 3.8.
Computer: (i) IBM PC, (ii) cluster.
Operating system: LINUX.
RAM: problem dependent (10Mb - 1Gb), typical working size < 100 Mb
Word size: 32, 64 bits
Keywords: Integrable super-systems, symmetries, recursions, classification, symbolic computation, REDUCE.
PACS: 02.30.Ik, 02.70.Wz, 12.60.Jv.
Classification: 4.3, 5, 11.1.

Nature of problem:
The program allows the classification of N ≥ 1 supersymmetric nonlinear scaling-invariant evolution equations {ft = φf, bt = φb} that admit infinitely many local symmetries propagated by recursion operators; here b(x, t; θ) is the set of bosonic super-fields and f(x; t; θ) are fermionic super-fields.

Solution method:
First, (half-)integer weights |f|, |b|, . . ., |Dt|, |Dx| ≡ 1 are assigned to all variables and derivatives and then pairs of commuting flows that are homogeneous w.r.t. these weights are constructed. Secondly, the seeds of higher symmetry sequences [2] for the systems are sorted out, and finally the recursion operators that generate the symmetries are obtained [3]. The intermediate algebraic systems upon the undetermined coefficients are solved by using [4].

Computation of symmetries of high differential order for very large evolutionary systems may cause memory restrictions. Additional size/time restrictions may occur if the homogeneity weights of some super-fields are non-positive, see section 1.2 of the LongWrite- Up.

Unusual features:
SsTools has been extensively tested using hundreds of PDE systems within three years on UNIX-based PC-machines. SsTools is applicable to the computation of symmetries, conservation laws, and Hamiltonian structures for N ≥ 1 evolutionary super-systems with any N. SsTools is also useful for performing extensive arithmetic of general nature including differentiations of super-field expressions.

Running time:
depends on the size and complexity of the input system and varies between seconds and minutes.

[1] http://lie.math.brocku.ca/crack/susy/sstools.red; The support package Crack is obtained from http://lie.math.brocku.ca/crack/src/crack.tar.gz
[2] P.J. Olver, Applications of Lie groups to differential equations, 2nd ed., Springer, Berlin, 1993.
[3] I. S. Krasil'shchik, P. H. M. Kersten, Symmetries and recursion operators for classical and supersymmetric differential equations, Kluwer, Dordrecht, 2000.
[4] T. Wolf, Applications of Crack in the classification of integrable systems, CRM Proc. Lecture Notes 37 (2004), 283-300.