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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_0Distribution 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 {f} that admit infinitely many local symmetries propagated by recursion operators; here _{t} = φ^{f}, b_{t} = φ^{b}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|, . . ., |D|, |_{t}D| ≡ 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]._{x} | ||

Restrictions: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. | ||

References: | ||

[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. |

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