On the biHamiltonian structure of the supersymmetric KdV hierarchies. A Lie superalgebraic approach

DOI10.1007/BF02108075zbMath0790.35097MaRDI QIDQ1313269

Carlo Morosi, Livio Pizzocchero

Publication date: 26 June 1994

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

reduction techniqueLie superalgebraloop algebraPoisson pencialsuperextension of the Drinfeld-Sokolov method

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Supersymmetric field theories in quantum mechanics (81T60) Superalgebras (17A70) Invariance and symmetry properties for PDEs on manifolds (58J70)

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New Bilinear Bäcklund Transformation and Lax Pair for the Supersymmetric Two-Boson Equation ⋮ Darboux transformations for supersymmetric Korteweg-de Vries equations ⋮ A fully supersymmetric AKNS theory ⋮ On the equivalence of two super Korteweg–deVries theories: A bi-Hamiltonian viewpoint ⋮ \(\text{osp}(3,2)\) and \(\text{gl}(3,3)\) supersymmetric KdV hierarchies ⋮ A supertrace identity and its applications to superintegrable systems ⋮ Super Camassa–Holm-type systems associated to the Kuper–Ramond–Schwarz superalgebra ⋮ Nonlinear super integrable couplings of super Broer-Kaup-Kupershmidt hierarchy and its super Hamiltonian structures ⋮ Supersymmetric Drinfeld–Sokolov reduction ⋮ SuSy 2. ⋮ Super extension of Bell polynomials with applications to supersymmetric equations

Cites Work

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• Superanalysis, I. Differential calculus
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• Reduction of Poisson manifolds
• A supersymmetric extension of the Kadomtsev-Petviashvili hierarchy
• Structure of basic Lie superalgebras and of their affine extensions
• Superspaces and supersymmetries
• Lie superalgebraic approach to super Toda lattice and generalized super KdV equations
• The bi-Hamiltonian structure of fully supersymmetric Korteweg-de Vries systems
• Drinfeld-Sokolov reduction on a simple Lie algebra from the bihamiltonian point of view
• Supersymmetric extension of the Korteweg–de Vries equation
• INTRODUCTION TO THE THEORY OF SUPERMANIFOLDS
• INTEGRABILITY AND BIHAMILTONIAN STRUCTURE OF THE EVEN ORDER SKDV HIERARCHIES
• Remarks on the complete integrability of dynamical systems with fermionic variables
• A simple model of the integrable Hamiltonian equation
• Lie superalgebras

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