Classification of integrable super-systems using the SsTools environment

Abstract

A classification problem is proposed for supersymmetric evolutionary PDE that satisfy the assumptions of nonlinearity and nondegeneracy. Four classes of nonlinear coupled boson-fermion systems are discovered under the homogeneity assumption |f|=|b|=|D_t|=1/2. 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.

MSC 35Q53,37K05,37K10,81T40; PACS 02.30.Ik,02.70.Wz,12.60.Jv; Comput. Phys. Commun. (2007), 26 pages (accepted)

References in corpus (4)

• Hamiltonian operators and l*-coverings
• Classification of polynomial integrable systems of mixed scalar and vector evolution equations. I
• A Mathematica Package for Computing N=2 Superfield Operator Product Expansions
• Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations

Cited by in corpus (9)

• Gardner's deformations of the N=2 supersymmetric a=4-KdV equation
• Hirota's virtual multi-soliton solutions of N=2 supersymmetric Korteweg-de Vries equations
• Involutive distributions of operator-valued evolutionary vector fields
• The right-hand side of the Jacobi identity: to be naught or not to be?
• Gardner's deformation of the Krasil'shchik-Kersten system
• Computing symmetries and recursion operators of evolutionary super-systems using the SsTools environment
• Gardner's deformations as generators of new integrable systems
• On the (non)removability of spectral parameters in $Z_2$-graded zero-curvature representations and its applications
• A convenient criterion under which Z_2-graded operators are Hamiltonian