The Gardner Category and Non-local Conservation Laws for N=1 Super KdV

Abstract

The non-local conserved quantities of N=1 Super KdV are obtained using a complete algebraic framework where the Gardner category is introduced. A fermionic substitution semigroup and the resulting Gardner category are defined and several propositions concerning their algebraic structure are proven. This algebraic framework allows to define general transformations between different nonlinear SUSY differential equations. We then introduce a SUSY ring extension to deal with the non-local conserved quantities of SKdV. The algebraic version of the non-local conserved quantities is solved in terms of the exponential function applied to the $D^{-1}$ of the local conserved quantities of SKdV. Finally the same formulas are shown to work for rapidly decreasing superfields.

arXiv comment17 pages

References in corpus (4)

• Nonlocal conservation laws in N=1,2 Supersymetric KdV equation
• An Operator Valued Extension of the Super KdV Equations
• The Heat Kernel Coefficients to the Matrix Schrödinger Operator
• Supersymmetric exact sequence, heat kernel and super KdV hierarchy

Cited by in corpus (8)

• Bosonization, Singularity Analysis, Nonlocal Symmetry Reductions and Exact Solutions of Supersymmetric KdV Equation
• Bosonization of Supersymmetric KdV equation
• On the non-abelian superalgebra spanned by the conserved quantities of N=1 supersymmetric Korteweg-de Vries equation
• The Hamiltonian structure of a coupled system derived from a supersymmetric breaking of Super KdV equations
• Gardner's deformations of the N=2 supersymmetric a=4-KdV equation
• Gardner's deformations of the Boussinesq equations
• Gardner's deformations of the graded Korteweg-de Vries equations revisited
• Hamiltonian structure of an operator valued extension of Super KdV equations