Classification of integrable super-systems using the SsTools environment

Please always quote using this URN: urn:nbn:de:0297-zib-11792
  • A classification problem is proposed for supersymmetric %scaling\/-\/in\-va\-ri\-ant evolutionary PDE that satisfy the assumptions of nonlinearity, nondegeneracy, and homogeneity. Four classes of nonlinear coupled boson\/-\/fermion systems are discovered under the weighting assumption $|f|=|b|=|D_t|=\oh$. The syntax of the \Reduce\ package \SsTools, which was used for intermediate computations, and the applicability of its procedures to the calculus of super\/-\/PDE are described.

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Metadaten
Author:A. V. Kiselev, Thomas Wolf
Document Type:ZIB-Report
Tag:Integrable super-systems; classifiaction; recursions; symmetries
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
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] / 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)
81-XX QUANTUM THEORY / 81Txx Quantum field theory; related classical field theories [See also 70Sxx] / 81T40 Two-dimensional field theories, conformal field theories, etc.
PACS-Classification:00.00.00 GENERAL / 02.00.00 Mathematical methods in physics / 02.30.-f Function theory, analysis / 02.30.Ik Integrable systems
Contributing Corporation:Max Planck Inst. for Mathematics, Bonn; Brock Univ., St.Catharines, Canada and ZIB Fellow
Date of first Publication:2010/07/07
Series (Serial Number):ZIB-Report (10-17)
ArXiv Id:http://arxiv.org/abs/nlin.SI/0609065
ISSN:1438-0064
Published in:Appeared under the title: "Classification of integrable super-equations by the SsTools environment" in: Comp. Phys. Comm., Vol. 177, no. 3 (2007) pp. 315-328