Integrable fermionic extensions of the Garnier system and the anharmonic oscillator
type: Item
instance of: scholarly article
title: Integrable fermionic extensions of the Garnier system and the anharmonic oscillator
zbMATH Open document ID: 1225.37082
author: Ruguang Zhou
author: Ying Kui
published in: Applied Mathematics and Computation
publication date: 2011-06-27T00:00:00Z
review text: In this paper the authors derive fermionic extensions of the Garnier system and the anharmonic oscillator, as well as their Lax representations, \(r\)-matrices and conversed integrals. Different from the classic Garnier system and the anharmonic oscillator, which are free Hamiltonian systems, these resulting fermionic extensions contain a nonholonomic constraint.
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 5913737
zbMATH Keywords: Lax representation
zbMATH Keywords: supersymmetric KdV equation
zbMATH Keywords: Garnier system
zbMATH Keywords: anharmonic oscillator
MaRDI profile type: Publication
full work available at URL: j.amc.2011.04.003
OpenAlex ID: W2023066464
cites work: The problem of integrable discretization: Hamiltonian approach
cites work: Integrable Hamiltonian systems connected with graded Lie algebras
cites work: Supersymmetric extension of the Korteweg–de Vries equation
cites work: Q4395160
cites work: The Finite-Dimensional Moser Type Reduction of Modified Boussinesq and Super-Korteweg-de Vries Hamiltonian Systems via the Gradient-Holonomic Algorithm and Dual Moment Maps. Part I
cites work: Hamiltonian finite-dimensional oscillator-type reductions of Lax-integrable superconformal hierarchies
cites work: Fermionic extensions of Painlevé equations
cites work: BINARY NONLINEARIZATION OF THE SUPER AKNS SYSTEM
cites work: Binary nonlinearization of the super AKNS system under an implicit symmetry constraint
cites work: The Bargmann symmetry constraint and binary nonlinearization of the super Dirac systems
cites work: Q3352574
cites work: An explicit symmetry constraint for the Lax pairs and the adjoint Lax pairs of AKNS systems
cites work: New Finite-Dimensional Integrable Systems by Symmetry Constraint of the KdV Equations
cites work: Q4847404
cites work: Adjoint Symmetry Constraints Leading to Binary Nonlinearization
cites work: Q4803247
cites work: An extended noncommutative KP hierarchy
cites work: Linear superposition principle applying to Hirota bilinear equations
DOI: 10.1016/J.AMC.2011.04.003
description: scientific article; zbMATH DE number 5913737