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

Please always quote using this URN: urn:nbn:de:0297-zib-8850

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.

Metadaten
Author:	Arthemy V. Kiselev, Thomas Wolf
Document Type:	ZIB-Report
MSC-Classification:	35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Qxx Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] / 35Q53 KdV-like equations (Korteweg-de Vries) [See also 37K10]
	37-XX DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] / 37Kxx Infinite-dimensional Hamiltonian systems [See also 35Axx, 35Qxx] / 37K05 Hamiltonian structures, symmetries, variational principles, conservation laws
	81-XX QUANTUM THEORY / 81Txx Quantum field theory; related classical field theories [See also 70Sxx] / 81T40 Two-dimensional field theories, conformal field theories, etc.
Date of first Publication:	2005/12/08
Series (Serial Number):	ZIB-Report (05-52)
ArXiv Id:	http://arxiv.org/abs/nlin.SI/0511056
ZIB-Reportnumber:	05-52
Published in:	Appeared under the title "On weakly non-local, nilpotent, and super-recursion operators for N=1 homogeneous super-equations", in: Proc. Int. Workshop Supersymmetries and Quantum Symmetries (SQS'05), Dubna, July 24--31, 2005. JINR, p. 231-237

Open Access