2005/04/19 by S. Andrea, A. Restuccia, A. Sotomayor · 18 citations
Physics and Astronomy · #Algebraic number #Black Holes and Theoretical Physics #Conservation law #Conserved quantity #Exponential function #Extension (predicate logic) #Korteweg–de Vries equation #Nonlinear Waves and Solitons #Nonlinear system #Quantum Mechanics and Non-Hermitian Physics #Supersymmetry #hep-th
paper · pdf · doi:10.1063/1.2073289
published in Journal of Mathematical Physics 46(10) (American Institute of Physics) · 17 pages
arxiv created 2005/04/19 · openalex publication_date 2005/10/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The nonlocal conserved quantities of the N=1 Super KdV are obtained using a Gardner map. A fermionic substitution semigroup and the resulting Gardner category are defined and several propositions concerning their algebraic structure are obtained. This algebraic framework makes it possible to define general transformations between different nonlinear SUSY differential equations. A SUSY ring extension is then introduced to deal with the nonlocal conserved quantities of SKdV. The algebraic version of the nonlocal 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.