On weakly non-local, nilpotent, and super-recursion operators for N=1 super-equations

Details On weakly non-local, nilpotent, and super-recursion operators for N=1 super-equations On weakly non-local, nilpotent, and super-recursion operators for N=1 super-equations

2005-11-26

arxiv.org/abs/nlin/0511056v1

Proc. Int. Workshop ``Supersymmetries and Quantum Symmetries'' (SQS'05), Dubna, July 24-31, 2005, JINR, p. 234-240

Nonlinear Sciences

Exactly Solvable and Integrable Systems

6 pages, no figures. Proc. Int. Workshop `Supersymmetries and Quantum Symmetries-05,' JINR, Dubna, 27-31 July 2005. MSC 2000:

Scientific paper

We consider nonlinear, scaling-invariant N=1 boson + fermion supersymmetric systems whose right-hand sides are homogeneous differential polynomials and satisfy some natural assumptions. We select the super-systems that admit infinitely many higher symmetries generated by recursion operators; we further restrict ourselves to the case when the dilaton dimensions of the bosonic and fermionic super-fields coincide and the weight of the time is half the weight of the spatial variable. We discover five systems that satisfy these assumptions; one system is transformed to the purely bosonic Burgers equation. We construct local, nilpotent, triangular, weakly non-local, and super-recursion operators for their symmetry algebras.

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